Different Based Math

[Harrisonized]

It's possible to calculate mathematical values using a variety of different bases.
http://hotmath.com/hotmath_help/alge...ent_bases.html

However, since brain plasticity is pretty much lost during childhood before the age of 9, a curious question is whether or not a person can effectively calculate using, say, binary code, after learning it at the age of 20. What happens if a young child is taught binary math and later on the person tries to learn base10 math as an adult? Would that person be unable to revert?

Recently I learned that when children learn many languages during childhood, they would be able to think in a larger range or view instead of being limited to certain concepts only expressed by the language. For example, knowing the word "blue" in different languages would allow you to perceive different shades of blue when the word is recited in different languages.

Thus, if a child learns both binary and base10 math and then base16 math at a young age, would she be able to become somewhat of a mathematical genius, or at least slightly faster at calculation, because she would be able to think in a range or view that ordinary people only taught base10 math would be able to perceive?

[Dusk]

I don't think it's a matter of learning math in one base or another. I learned everything in base 10 like everyone else, but I'm very proficient at working with numbers in different bases. It's just mental math skills, something I am lucky to have. I remember learning these conversion tricks in my CS class in high school to solve problems like 153(base 16) * 82 (base16) where they'd tell us to convert to base 10, multiply, and convert back, while I'd simply multiply everything in base 16.

As far as being a mathematical genius, being good at basic arithmetic doesn't stop me from failing miserably at Calculus and Linear Algebra. Math isn't my thing at all.

[Harrisonized]

I don't think it's a matter of learning math in one base or another. I learned everything in base 10 like everyone else, but I'm very proficient at working with numbers in different bases. It's just mental math skills, something I am lucky to have. I remember learning these conversion tricks in my CS class in high school to solve problems like 153(base 16) * 82 (base16) where they'd tell us to convert to base 10, multiply, and convert back,

Well you see... that's why I was wondering. Because *most* people I hear of working with different based math will need some form of conversion, and that's not effectively using it.

while I'd simply multiply everything in base 16.

That's very interesting. However, since I'll compare base16 math to a second language, would you say you calculate in base16 with the same speed as you can handle base10 math or would you say your base16 math is slower, if not a lot, slightly.

As far as being a mathematical genius, being good at basic arithmetic doesn't stop me from failing miserably at Calculus and Linear Algebra. Math isn't my thing at all.

So are you just confused at Calculus and Linear Algebra or did learning two different bases screw you up a bit?

[Nikkey]

It'll only make it easier to understand bases. But will it help with anything else?

[Stereo]

That's very interesting. However, since I'll compare base16 math to a second language, would you say you calculate in base16 with the same speed as you can handle base10 math or would you say your base16 math is slower, if not a lot, slightly.

This isn't too bad so long as you remember the basic times tables.

\	1	2	3	4	5	6	7	8	9	a	b	c	d	e	f
1	1	2	3	4	5	6	7	8	9	a	b	c	d	e	f
2	2	4	6	8	a	c	e	10	12	14	16	18	1a	1c	1e
3	3	6	9	c	f	12	15	18	1b	1e	21	24	27	3a	3d
4	4	8	c	10	14	18	1c	20	24	28	2c	30	34	38	3c
...

Then you just do the same thing as normally in math

  23
x 14
====
  9c
 23
 2bc

Standard "tricks" still apply, just shifted to account for the change in base. Like 16 is divisible by 2, 4, 8 - so those tables are easy. (like 5 times tables in base 10). And since F is the (b-1) number, multiplying it looks a lot similar - 5*F = 4B, A*F = 96, etc. - the digits add up to multiples of F.

[KajitiSouls]

It's not so hard doing basic adding/subtracting in different base numbers. The real grind for me is knowing what the exact value is. So say I had two values in base two: 10001 and 1011100. Add them together and I have 1101101. But what is that in base 10?

And like Stereo said, I'm very sure we all had to memorize the multiplication table. I don't think there's any easier way.

[Chompy]

I am with Harrisonized on this.
Ambassador's children sometimes spend so much time that by their teens they can speak multiple languages so fluently that they literally slip and weave between languages mid-speech.
Apparently their ability word-smith (say EXACTLY what they mean) is much much higher.
I can imagine much to the same for math.

[Dusk]

Well you see... that's why I was wondering. Because *most* people I hear of working with different based math will need some form of conversion, and that's not effectively using it.

That's very interesting. However, since I'll compare base16 math to a second language, would you say you calculate in base16 with the same speed as you can handle base10 math or would you say your base16 math is slower, if not a lot, slightly.

I'd say probably with the effectiveness of a foreign language. It takes a little bit to mentally create a multiplication table. It'd probably be faster if I had learned hex as a child, but I really don't see the practicality of teaching multiple bases, since they aren't used often enough.

So are you just confused at Calculus and Linear Algebra or did learning two different bases screw you up a bit?

Just confused. Not as good at logic and stuff as I am at simple number manipulation.

[Nikkey]

Really though, I can't see anything but proper understanding of bases by doing this. What will it help you knowing base 3? Will you achieve something? :x

AllBasesAreBelongToMe

In base 2:

1	10
10	100

In base 3:

1	2	10
2	11	20
10	20	100

In base 4:

1	2	3	10
2	10	12	20
3	12	21	30
10	20	30	100

In base 5:

1	2	3	4	10
2	4	11	13	20
3	11	14	22	30
4	13	22	31	40
10	20	30	40	100

In base 6:

1	2	3	4	5	10
2	4	10	12	14	20
3	10	13	20	23	30
4	12	20	24	32	40
5	14	23	32	41	50
10	20	30	40	50	100

In base 7:

1	2	3	4	5	6	10
2	4	6	11	13	15	20
3	6	12	15	21	24	30
4	11	15	22	26	33	40
5	13	21	26	34	42	50
6	15	24	33	42	51	60
10	20	30	40	50	60	100

In base 8:

1	2	3	4	5	6	7	10
2	4	6	10	12	14	16	20
3	6	11	14	17	22	25	30
4	10	14	20	24	30	34	40
5	12	17	24	31	36	43	50
6	14	22	30	36	44	52	60
7	16	25	34	43	52	61	70
10	20	30	40	50	60	70	100

In base 9:

1	2	3	4	5	6	7	8	10
2	4	6	8	11	13	15	17	20
3	6	10	13	16	20	23	26	30
4	8	13	17	22	26	31	35	40
5	11	16	22	27	33	38	44	50
6	13	20	26	33	40	46	53	60
7	15	23	31	38	46	54	62	70
8	17	26	35	44	53	62	71	80
10	20	30	40	50	60	70	80	100

In base 10:

1	2	3	4	5	6	7	8	9	10
2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50
6	12	18	24	30	36	42	48	54	60
7	14	21	28	35	42	49	56	63	70
8	16	24	32	40	48	56	64	72	80
9	18	27	36	45	54	63	72	81	90
10	20	30	40	50	60	70	80	90	100

In base 11:

1	2	3	4	5	6	7	8	9	A	10
2	4	6	8	A	11	13	15	17	19	20
3	6	9	11	14	17	1A	22	25	28	30
4	8	11	15	19	22	26	2A	33	37	40
5	A	14	19	23	28	32	37	41	46	50
6	11	17	22	28	33	39	44	4A	55	60
7	13	1A	26	32	39	45	51	58	64	70
8	15	22	2A	37	44	51	59	66	73	80
9	17	25	33	41	4A	58	66	74	82	90
A	19	28	37	46	55	64	73	82	91	A0
10	20	30	40	50	60	70	80	90	A0	100

In base 12:

1	2	3	4	5	6	7	8	9	A	B	10
2	4	6	8	A	10	12	14	16	18	1A	20
3	6	9	10	13	16	19	20	23	26	29	30
4	8	10	14	18	20	24	28	30	34	38	40
5	A	13	18	21	26	2B	34	39	42	47	50
6	10	16	20	26	30	36	40	46	50	56	60
7	12	19	24	2B	36	41	48	53	5A	65	70
8	14	20	28	34	40	48	54	60	68	74	80
9	16	23	30	39	46	53	60	69	76	83	90
A	18	26	34	42	50	5A	68	76	84	92	A0
B	1A	29	38	47	56	65	74	83	92	A1	B0
10	20	30	40	50	60	70	80	90	A0	B0	100

In base 13:

1	2	3	4	5	6	7	8	9	A	B	C	10
2	4	6	8	A	C	11	13	15	17	19	1B	20
3	6	9	C	12	15	18	1B	21	24	27	2A	30
4	8	C	13	17	1B	22	26	2A	31	35	39	40
5	A	12	17	1C	24	29	31	36	3B	43	48	50
6	C	15	1B	24	2A	33	39	42	48	51	57	60
7	11	18	22	29	33	3A	44	4B	55	5C	66	70
8	13	1B	26	31	39	44	4C	57	62	6A	75	80
9	15	21	2A	36	42	4B	57	63	6C	78	84	90
A	17	24	31	3B	48	55	62	6C	79	86	93	A0
B	19	27	35	43	51	5C	6A	78	86	94	A2	B0
C	1B	2A	39	48	57	66	75	84	93	A2	B1	C0
10	20	30	40	50	60	70	80	90	A0	B0	C0	100

In base 14:

1	2	3	4	5	6	7	8	9	A	B	C	D	10
2	4	6	8	A	C	10	12	14	16	18	1A	1C	20
3	6	9	C	11	14	17	1A	1D	22	25	28	2B	30
4	8	C	12	16	1A	20	24	28	2C	32	36	3A	40
5	A	11	16	1B	22	27	2C	33	38	3D	44	49	50
6	C	14	1A	22	28	30	36	3C	44	4A	52	58	60
7	10	17	20	27	30	37	40	47	50	57	60	67	70
8	12	1A	24	2C	36	40	48	52	5A	64	6C	76	80
9	14	1D	28	33	3C	47	52	5B	66	71	7A	85	90
A	16	22	2C	38	44	50	5A	66	72	7C	88	94	A0
B	18	25	32	3D	4A	57	64	71	7C	89	96	A3	B0
C	1A	28	36	44	52	60	6C	7A	88	96	A4	B2	C0
D	1C	2B	3A	49	58	67	76	85	94	A3	B2	C1	D0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	100

In base 15:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	10
2	4	6	8	A	C	E	11	13	15	17	19	1B	1D	20
3	6	9	C	10	13	16	19	1C	20	23	26	29	2C	30
4	8	C	11	15	19	1D	22	26	2A	2E	33	37	3B	40
5	A	10	15	1A	20	25	2A	30	35	3A	40	45	4A	50
6	C	13	19	20	26	2C	33	39	40	46	4C	53	59	60
7	E	16	1D	25	2C	34	3B	43	4A	52	59	61	68	70
8	11	19	22	2A	33	3B	44	4C	55	5D	66	6E	77	80
9	13	1C	26	30	39	43	4C	56	60	69	73	7C	86	90
A	15	20	2A	35	40	4A	55	60	6A	75	80	8A	95	A0
B	17	23	2E	3A	46	52	5D	69	75	81	8C	98	A4	B0
C	19	26	33	40	4C	59	66	73	80	8C	99	A6	B3	C0
D	1B	29	37	45	53	61	6E	7C	8A	98	A6	B4	C2	D0
E	1D	2C	3B	4A	59	68	77	86	95	A4	B3	C2	D1	E0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	100

In base 16:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	10
2	4	6	8	A	C	E	10	12	14	16	18	1A	1C	1E	20
3	6	9	C	F	12	15	18	1B	1E	21	24	27	2A	2D	30
4	8	C	10	14	18	1C	20	24	28	2C	30	34	38	3C	40
5	A	F	14	19	1E	23	28	2D	32	37	3C	41	46	4B	50
6	C	12	18	1E	24	2A	30	36	3C	42	48	4E	54	5A	60
7	E	15	1C	23	2A	31	38	3F	46	4D	54	5B	62	69	70
8	10	18	20	28	30	38	40	48	50	58	60	68	70	78	80
9	12	1B	24	2D	36	3F	48	51	5A	63	6C	75	7E	87	90
A	14	1E	28	32	3C	46	50	5A	64	6E	78	82	8C	96	A0
B	16	21	2C	37	42	4D	58	63	6E	79	84	8F	9A	A5	B0
C	18	24	30	3C	48	54	60	6C	78	84	90	9C	A8	B4	C0
D	1A	27	34	41	4E	5B	68	75	82	8F	9C	A9	B6	C3	D0
E	1C	2A	38	46	54	62	70	7E	8C	9A	A8	B6	C4	D2	E0
F	1E	2D	3C	4B	5A	69	78	87	96	A5	B4	C3	D2	E1	F0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	100

In base 17:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	G	10
2	4	6	8	A	C	E	G	11	13	15	17	19	1B	1D	1F	20
3	6	9	C	F	11	14	17	1A	1D	1G	22	25	28	2B	2E	30
4	8	C	G	13	17	1B	1F	22	26	2A	2E	31	35	39	3D	40
5	A	F	13	18	1D	21	26	2B	2G	34	39	3E	42	47	4C	50
6	C	11	17	1D	22	28	2E	33	39	3F	44	4A	4G	55	5B	60
7	E	14	1B	21	28	2F	35	3C	42	49	4G	56	5D	63	6A	70
8	G	17	1F	26	2E	35	3D	44	4C	53	5B	62	6A	71	79	80
9	11	1A	22	2B	33	3C	44	4D	55	5E	66	6F	77	7G	88	90
A	13	1D	26	2G	39	42	4C	55	5F	68	71	7B	84	8E	97	A0
B	15	1G	2A	34	3F	49	53	5E	68	72	7D	87	91	9C	A6	B0
C	17	22	2E	39	44	4G	5B	66	71	7D	88	93	9F	AA	B5	C0
D	19	25	31	3E	4A	56	62	6F	7B	87	93	9G	AC	B8	C4	D0
E	1B	28	35	42	4G	5D	6A	77	84	91	9F	AC	B9	C6	D3	E0
F	1D	2B	39	47	55	63	71	7G	8E	9C	AA	B8	C6	D4	E2	F0
G	1F	2E	3D	4C	5B	6A	79	88	97	A6	B5	C4	D3	E2	F1	G0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	G0	100

In base 18:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	G	H	10
2	4	6	8	A	C	E	G	10	12	14	16	18	1A	1C	1E	1G	20
3	6	9	C	F	10	13	16	19	1C	1F	20	23	26	29	2C	2F	30
4	8	C	G	12	16	1A	1E	20	24	28	2C	2G	32	36	3A	3E	40
5	A	F	12	17	1C	1H	24	29	2E	31	36	3B	3G	43	48	4D	50
6	C	10	16	1C	20	26	2C	30	36	3C	40	46	4C	50	56	5C	60
7	E	13	1A	1H	26	2D	32	39	3G	45	4C	51	58	5F	64	6B	70
8	G	16	1E	24	2C	32	3A	40	48	4G	56	5E	64	6C	72	7A	80
9	10	19	20	29	30	39	40	49	50	59	60	69	70	79	80	89	90
A	12	1C	24	2E	36	3G	48	50	5A	62	6C	74	7E	86	8G	98	A0
B	14	1F	28	31	3C	45	4G	59	62	6D	76	7H	8A	93	9E	A7	B0
C	16	20	2C	36	40	4C	56	60	6C	76	80	8C	96	A0	AC	B6	C0
D	18	23	2G	3B	46	51	5E	69	74	7H	8C	97	A2	AF	BA	C5	D0
E	1A	26	32	3G	4C	58	64	70	7E	8A	96	A2	AG	BC	C8	D4	E0
F	1C	29	36	43	50	5F	6C	79	86	93	A0	AF	BC	C9	D6	E3	F0
G	1E	2C	3A	48	56	64	72	80	8G	9E	AC	BA	C8	D6	E4	F2	G0
H	1G	2F	3E	4D	5C	6B	7A	89	98	A7	B6	C5	D4	E3	F2	G1	H0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	G0	H0	100

In base 19:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	G	H	I	10
2	4	6	8	A	C	E	G	I	11	13	15	17	19	1B	1D	1F	1H	20
3	6	9	C	F	I	12	15	18	1B	1E	1H	21	24	27	2A	2D	2G	30
4	8	C	G	11	15	19	1D	1H	22	26	2A	2E	2I	33	37	3B	3F	40
5	A	F	11	16	1B	1G	22	27	2C	2H	33	38	3D	3I	44	49	4E	50
6	C	I	15	1B	1H	24	2A	2G	33	39	3F	42	48	4E	51	57	5D	60
7	E	12	19	1G	24	2B	2I	36	3D	41	48	4F	53	5A	5H	65	6C	70
8	G	15	1D	22	2A	2I	37	3F	44	4C	51	59	5H	66	6E	73	7B	80
9	I	18	1H	27	2G	36	3F	45	4E	54	5D	63	6C	72	7B	81	8A	90
A	11	1B	22	2C	33	3D	44	4E	55	5F	66	6G	77	7H	88	8I	99	A0
B	13	1E	26	2H	39	41	4C	54	5F	67	6I	7A	82	8D	95	9G	A8	B0
C	15	1H	2A	33	3F	48	51	5D	66	6I	7B	84	8G	99	A2	AE	B7	C0
D	17	21	2E	38	42	4F	59	63	6G	7A	84	8H	9B	A5	AI	BC	C6	D0
E	19	24	2I	3D	48	53	5H	6C	77	82	8G	9B	A6	B1	BF	CA	D5	E0
F	1B	27	33	3I	4E	5A	66	72	7H	8D	99	A5	B1	BG	CC	D8	E4	F0
G	1D	2A	37	44	51	5H	6E	7B	88	95	A2	AI	BF	CC	D9	E6	F3	G0
H	1F	2D	3B	49	57	65	73	81	8I	9G	AE	BC	CA	D8	E6	F4	G2	H0
I	1H	2G	3F	4E	5D	6C	7B	8A	99	A8	B7	C6	D5	E4	F3	G2	H1	I0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	G0	H0	I0	100

In base 20:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	G	H	I	J	10
2	4	6	8	A	C	E	G	I	10	12	14	16	18	1A	1C	1E	1G	1I	20
3	6	9	C	F	I	11	14	17	1A	1D	1G	1J	22	25	28	2B	2E	2H	30
4	8	C	G	10	14	18	1C	1G	20	24	28	2C	2G	30	34	38	3C	3G	40
5	A	F	10	15	1A	1F	20	25	2A	2F	30	35	3A	3F	40	45	4A	4F	50
6	C	I	14	1A	1G	22	28	2E	30	36	3C	3I	44	4A	4G	52	58	5E	60
7	E	11	18	1F	22	29	2G	33	3A	3H	44	4B	4I	55	5C	5J	66	6D	70
8	G	14	1C	20	28	2G	34	3C	40	48	4G	54	5C	60	68	6G	74	7C	80
9	I	17	1G	25	2E	33	3C	41	4A	4J	58	5H	66	6F	74	7D	82	8B	90
A	10	1A	20	2A	30	3A	40	4A	50	5A	60	6A	70	7A	80	8A	90	9A	A0
B	12	1D	24	2F	36	3H	48	4J	5A	61	6C	73	7E	85	8G	97	9I	A9	B0
C	14	1G	28	30	3C	44	4G	58	60	6C	74	7G	88	90	9C	A4	AG	B8	C0
D	16	1J	2C	35	3I	4B	54	5H	6A	73	7G	89	92	9F	A8	B1	BE	C7	D0
E	18	22	2G	3A	44	4I	5C	66	70	7E	88	92	9G	AA	B4	BI	CC	D6	E0
F	1A	25	30	3F	4A	55	60	6F	7A	85	90	9F	AA	B5	C0	CF	DA	E5	F0
G	1C	28	34	40	4G	5C	68	74	80	8G	9C	A8	B4	C0	CG	DC	E8	F4	G0
H	1E	2B	38	45	52	5J	6G	7D	8A	97	A4	B1	BI	CF	DC	E9	F6	G3	H0
I	1G	2E	3C	4A	58	66	74	82	90	9I	AG	BE	CC	DA	E8	F6	G4	H2	I0
J	1I	2H	3G	4F	5E	6D	7C	8B	9A	A9	B8	C7	D6	E5	F4	G3	H2	I1	J0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	G0	H0	I0	J0	100

In base 21:

1	2	3	4	5	6	7	8	9	A	B	C	D	E	F	G	H	I	J	K	10
2	4	6	8	A	C	E	G	I	K	11	13	15	17	19	1B	1D	1F	1H	1J	20
3	6	9	C	F	I	10	13	16	19	1C	1F	1I	20	23	26	29	2C	2F	2I	30
4	8	C	G	K	13	17	1B	1F	1J	22	26	2A	2E	2I	31	35	39	3D	3H	40
5	A	F	K	14	19	1E	1J	23	28	2D	2I	32	37	3C	3H	41	46	4B	4G	50
6	C	I	13	19	1F	20	26	2C	2I	33	39	3F	40	46	4C	4I	53	59	5F	60
7	E	10	17	1E	20	27	2E	30	37	3E	40	47	4E	50	57	5E	60	67	6E	70
8	G	13	1B	1J	26	2E	31	39	3H	44	4C	4K	57	5F	62	6A	6I	75	7D	80
9	I	16	1F	23	2C	30	39	3I	46	4F	53	5C	60	69	6I	76	7F	83	8C	90
A	K	19	1J	28	2I	37	3H	46	4G	55	5F	64	6E	73	7D	82	8C	91	9B	A0
B	11	1C	22	2D	33	3E	44	4F	55	5G	66	6H	77	7I	88	8J	99	9K	AA	B0
C	13	1F	26	2I	39	40	4C	53	5F	66	6I	79	80	8C	93	9F	A6	AI	B9	C0
D	15	1I	2A	32	3F	47	4K	5C	64	6H	79	81	8E	96	9J	AB	B3	BG	C8	D0
E	17	20	2E	37	40	4E	57	60	6E	77	80	8E	97	A0	AE	B7	C0	CE	D7	E0
F	19	23	2I	3C	46	50	5F	69	73	7I	8C	96	A0	AF	B9	C3	CI	DC	E6	F0
G	1B	26	31	3H	4C	57	62	6I	7D	88	93	9J	AE	B9	C4	CK	DF	EA	F5	G0
H	1D	29	35	41	4I	5E	6A	76	82	8J	9F	AB	B7	C3	CK	DG	EC	F8	G4	H0
I	1F	2C	39	46	53	60	6I	7F	8C	99	A6	B3	C0	CI	DF	EC	F9	G6	H3	I0
J	1H	2F	3D	4B	59	67	75	83	91	9K	AI	BG	CE	DC	EA	F8	G6	H4	I2	J0
K	1J	2I	3H	4G	5F	6E	7D	8C	9B	AA	B9	C8	D7	E6	F5	G4	H3	I2	J1	K0
10	20	30	40	50	60	70	80	90	A0	B0	C0	D0	E0	F0	G0	H0	I0	J0	K0	100

In base 22:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

10

2

4

6

8

A

C

E

G

I

K

10

12

14

16

18

1A

1C

1E

1G

1I

1K

20

3

6

9

C

F

I

L

12

15

18

1B

1E

1H

1K

21

24

27

2A

2D

2G

2J

30

4

8

C

G

K

12

16

1A

1E

1I

20

24

28

2C

2G

2K

32

36

3A

3E

3I

40

5

A

F

K

13

18

1D

1I

21

26

2B

2G

2L

34

39

3E

3J

42

47

4C

4H

50

6

C

I

12

18

1E

1K

24

2A

2G

30

36

3C

3I

42

48

4E

4K

54

5A

5G

60

7

E

L

16

1D

1K

25

2C

2J

34

3B

3I

43

4A

4H

52

59

5G

61

68

6F

70

8

G

12

1A

1I

24

2C

2K

36

3E

40

48

4G

52

5A

5I

64

6C

6K

76

7E

80

9

I

15

1E

21

2A

2J

36

3F

42

4B

4K

57

5G

63

6C

6L

78

7H

84

8D

90

A

K

18

1I

26

2G

34

3E

42

4C

50

5A

5K

68

6I

76

7G

84

8E

92

9C

A0

B

10

1B

20

2B

30

3B

40

4B

50

5B

60

6B

70

7B

80

8B

90

9B

A0

AB

B0

C

12

1E

24

2G

36

3I

48

4K

5A

60

6C

72

7E

84

8G

96

9I

A8

AK

BA

C0

D

14

1H

28

2L

3C

43

4G

57

5K

6B

72

7F

86

8J

9A

A1

AE

B5

BI

C9

D0

E

16

1K

2C

34

3I

4A

52

5G

68

70

7E

86

8K

9C

A4

AI

BA

C2

CG

D8

E0

F

18

21

2G

39

42

4H

5A

63

6I

7B

84

8J

9C

A5

AK

BD

C6

CL

DE

E7

F0

G

1A

24

2K

3E

48

52

5I

6C

76

80

8G

9A

A4

AK

BE

C8

D2

DI

EC

F6

G0

H

1C

27

32

3J

4E

59

64

6L

7G

8B

96

A1

AI

BD

C8

D3

DK

EF

FA

G5

H0

I

1E

2A

36

42

4K

5G

6C

78

84

90

9I

AE

BA

C6

D2

DK

EG

FC

G8

H4

I0

J

1G

2D

3A

47

54

61

6K

7H

8E

9B

A8

B5

C2

CL

DI

EF

FC

G9

H6

I3

J0

K

1I

2G

3E

4C

5A

68

76

84

92

A0

AK

BI

CG

DE

EC

FA

G8

H6

I4

J2

K0

L

1K

2J

3I

4H

5G

6F

7E

8D

9C

AB

BA

C9

D8

E7

F6

G5

H4

I3

J2

K1

L0

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

100

In base 23:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

10

2

4

6

8

A

C

E

G

I

K

M

11

13

15

17

19

1B

1D

1F

1H

1J

1L

20

3

6

9

C

F

I

L

11

14

17

1A

1D

1G

1J

1M

22

25

28

2B

2E

2H

2K

30

4

8

C

G

K

11

15

19

1D

1H

1L

22

26

2A

2E

2I

2M

33

37

3B

3F

3J

40

5

A

F

K

12

17

1C

1H

1M

24

29

2E

2J

31

36

3B

3G

3L

43

48

4D

4I

50

6

C

I

11

17

1D

1J

22

28

2E

2K

33

39

3F

3L

44

4A

4G

4M

55

5B

5H

60

7

E

L

15

1C

1J

23

2A

2H

31

38

3F

3M

46

4D

4K

54

5B

5I

62

69

6G

70

8

G

11

19

1H

22

2A

2I

33

3B

3J

44

4C

4K

55

5D

5L

66

6E

6M

77

7F

80

9

I

14

1D

1M

28

2H

33

3C

3L

47

4G

52

5B

5K

66

6F

71

7A

7J

85

8E

90

A

K

17

1H

24

2E

31

3B

3L

48

4I

55

5F

62

6C

6M

79

7J

86

8G

93

9D

A0

B

M

1A

1L

29

2K

38

3J

47

4I

56

5H

65

6G

74

7F

83

8E

92

9D

A1

AC

B0

C

11

1D

22

2E

33

3F

44

4G

55

5H

66

6I

77

7J

88

8K

99

9L

AA

AM

BB

C0

D

13

1G

26

2J

39

3M

4C

52

5F

65

6I

78

7L

8B

91

9E

A4

AH

B7

BK

CA

D0

E

15

1J

2A

31

3F

46

4K

5B

62

6G

77

7L

8C

93

9H

A8

AM

BD

C4

CI

D9

E0

F

17

1M

2E

36

3L

4D

55

5K

6C

74

7J

8B

93

9I

AA

B2

BH

C9

D1

DG

E8

F0

G

19

22

2I

3B

44

4K

5D

66

6M

7F

88

91

9H

AA

B3

BJ

CC

D5

DL

EE

F7

G0

H

1B

25

2M

3G

4A

54

5L

6F

79

83

8K

9E

A8

B2

BJ

CD

D7

E1

EI

FC

G6

H0

I

1D

28

33

3L

4G

5B

66

71

7J

8E

99

A4

AM

BH

CC

D7

E2

EK

FF

GA

H5

I0

J

1F

2B

37

43

4M

5I

6E

7A

86

92

9L

AH

BD

C9

D5

E1

EK

FG

GC

H8

I4

J0

K

1H

2E

3B

48

55

62

6M

7J

8G

9D

AA

B7

C4

D1

DL

EI

FF

GC

H9

I6

J3

K0

L

1J

2H

3F

4D

5B

69

77

85

93

A1

AM

BK

CI

DG

EE

FC

GA

H8

I6

J4

K2

L0

M

1L

2K

3J

4I

5H

6G

7F

8E

9D

AC

BB

CA

D9

E8

F7

G6

H5

I4

J3

K2

L1

M0

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

100

In base 24:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

10

2

4

6

8

A

C

E

G

I

K

M

10

12

14

16

18

1A

1C

1E

1G

1I

1K

1M

20

3

6

9

C

F

I

L

10

13

16

19

1C

1F

1I

1L

20

23

26

29

2C

2F

2I

2L

30

4

8

C

G

K

10

14

18

1C

1G

1K

20

24

28

2C

2G

2K

30

34

38

3C

3G

3K

40

5

A

F

K

11

16

1B

1G

1L

22

27

2C

2H

2M

33

38

3D

3I

3N

44

49

4E

4J

50

6

C

I

10

16

1C

1I

20

26

2C

2I

30

36

3C

3I

40

46

4C

4I

50

56

5C

5I

60

7

E

L

14

1B

1I

21

28

2F

2M

35

3C

3J

42

49

4G

4N

56

5D

5K

63

6A

6H

70

8

G

10

18

1G

20

28

2G

30

38

3G

40

48

4G

50

58

5G

60

68

6G

70

78

7G

80

9

I

13

1C

1L

26

2F

30

39

3I

43

4C

4L

56

5F

60

69

6I

73

7C

7L

86

8F

90

A

K

16

1G

22

2C

2M

38

3I

44

4E

50

5A

5K

66

6G

72

7C

7M

88

8I

94

9E

A0

B

M

19

1K

27

2I

35

3G

43

4E

51

5C

5N

6A

6L

78

7J

86

8H

94

9F

A2

AD

B0

C

10

1C

20

2C

30

3C

40

4C

50

5C

60

6C

70

7C

80

8C

90

9C

A0

AC

B0

BC

C0

D

12

1F

24

2H

36

3J

48

4L

5A

5N

6C

71

7E

83

8G

95

9I

A7

AK

B9

BM

CB

D0

E

14

1I

28

2M

3C

42

4G

56

5K

6A

70

7E

84

8I

98

9M

AC

B2

BG

C6

CK

DA

E0

F

16

1L

2C

33

3I

49

50

5F

66

6L

7C

83

8I

99

A0

AF

B6

BL

CC

D3

DI

E9

F0

G

18

20

2G

38

40

4G

58

60

6G

78

80

8G

98

A0

AG

B8

C0

CG

D8

E0

EG

F8

G0

H

1A

23

2K

3D

46

4N

5G

69

72

7J

8C

95

9M

AF

B8

C1

CI

DB

E4

EL

FE

G7

H0

I

1C

26

30

3I

4C

56

60

6I

7C

86

90

9I

AC

B6

C0

CI

DC

E6

F0

FI

GC

H6

I0

J

1E

29

34

3N

4I

5D

68

73

7M

8H

9C

A7

B2

BL

CG

DB

E6

F1

FK

GF

HA

I5

J0

K

1G

2C

38

44

50

5K

6G

7C

88

94

A0

AK

BG

CC

D8

E4

F0

FK

GG

HC

I8

J4

K0

L

1I

2F

3C

49

56

63

70

7L

8I

9F

AC

B9

C6

D3

E0

EL

FI

GF

HC

I9

J6

K3

L0

M

1K

2I

3G

4E

5C

6A

78

86

94

A2

B0

BM

CK

DI

EG

FE

GC

HA

I8

J6

K4

L2

M0

N

1M

2L

3K

4J

5I

6H

7G

8F

9E

AD

BC

CB

DA

E9

F8

G7

H6

I5

J4

K3

L2

M1

N0

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

100

In base 25:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

10

2

4

6

8

A

C

E

G

I

K

M

O

11

13

15

17

19

1B

1D

1F

1H

1J

1L

1N

20

3

6

9

C

F

I

L

O

12

15

18

1B

1E

1H

1K

1N

21

24

27

2A

2D

2G

2J

2M

30

4

8

C

G

K

O

13

17

1B

1F

1J

1N

22

26

2A

2E

2I

2M

31

35

39

3D

3H

3L

40

5

A

F

K

10

15

1A

1F

1K

20

25

2A

2F

2K

30

35

3A

3F

3K

40

45

4A

4F

4K

50

6

C

I

O

15

1B

1H

1N

24

2A

2G

2M

33

39

3F

3L

42

48

4E

4K

51

57

5D

5J

60

7

E

L

13

1A

1H

1O

26

2D

2K

32

39

3G

3N

45

4C

4J

51

58

5F

5M

64

6B

6I

70

8

G

O

17

1F

1N

26

2E

2M

35

3D

3L

44

4C

4K

53

5B

5J

62

6A

6I

71

79

7H

80

9

I

12

1B

1K

24

2D

2M

36

3F

3O

48

4H

51

5A

5J

63

6C

6L

75

7E

7N

87

8G

90

A

K

15

1F

20

2A

2K

35

3F

40

4A

4K

55

5F

60

6A

6K

75

7F

80

8A

8K

95

9F

A0

B

M

18

1J

25

2G

32

3D

3O

4A

4L

57

5I

64

6F

71

7C

7N

89

8K

96

9H

A3

AE

B0

C

O

1B

1N

2A

2M

39

3L

48

4K

57

5J

66

6I

75

7H

84

8G

93

9F

A2

AE

B1

BD

C0

D

11

1E

22

2F

33

3G

44

4H

55

5I

66

6J

77

7K

88

8L

99

9M

AA

AN

BB

BO

CC

D0

E

13

1H

26

2K

39

3N

4C

51

5F

64

6I

77

7L

8A

8O

9D

A2

AG

B5

BJ

C8

CM

DB

E0

F

15

1K

2A

30

3F

45

4K

5A

60

6F

75

7K

8A

90

9F

A5

AK

BA

C0

CF

D5

DK

EA

F0

G

17

1N

2E

35

3L

4C

53

5J

6A

71

7H

88

8O

9F

A6

AM

BD

C4

CK

DB

E2

EI

F9

G0

H

19

21

2I

3A

42

4J

5B

63

6K

7C

84

8L

9D

A5

AM

BE

C6

CN

DF

E7

EO

FG

G8

H0

I

1B

24

2M

3F

48

51

5J

6C

75

7N

8G

99

A2

AK

BD

C6

CO

DH

EA

F3

FL

GE

H7

I0

J

1D

27

31

3K

4E

58

62

6L

7F

89

93

9M

AG

BA

C4

CN

DH

EB

F5

FO

GI

HC

I6

J0

K

1F

2A

35

40

4K

5F

6A

75

80

8K

9F

AA

B5

C0

CK

DF

EA

F5

G0

GK

HF

IA

J5

K0

L

1H

2D

39

45

51

5M

6I

7E

8A

96

A2

AN

BJ

CF

DB

E7

F3

FO

GK

HG

IC

J8

K4

L0

M

1J

2G

3D

4A

57

64

71

7N

8K

9H

AE

BB

C8

D5

E2

EO

FL

GI

HF

IC

J9

K6

L3

M0

N

1L

2J

3H

4F

5D

6B

79

87

95

A3

B1

BO

CM

DK

EI

FG

GE

HC

IA

J8

K6

L4

M2

N0

O

1N

2M

3L

4K

5J

6I

7H

8G

9F

AE

BD

CC

DB

EA

F9

G8

H7

I6

J5

K4

L3

M2

N1

O0

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

100

In base 26:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

10

2

4

6

8

A

C

E

G

I

K

M

O

10

12

14

16

18

1A

1C

1E

1G

1I

1K

1M

1O

20

3

6

9

C

F

I

L

O

11

14

17

1A

1D

1G

1J

1M

1P

22

25

28

2B

2E

2H

2K

2N

30

4

8

C

G

K

O

12

16

1A

1E

1I

1M

20

24

28

2C

2G

2K

2O

32

36

3A

3E

3I

3M

40

5

A

F

K

P

14

19

1E

1J

1O

23

28

2D

2I

2N

32

37

3C

3H

3M

41

46

4B

4G

4L

50

6

C

I

O

14

1A

1G

1M

22

28

2E

2K

30

36

3C

3I

3O

44

4A

4G

4M

52

58

5E

5K

60

7

E

L

12

19

1G

1N

24

2B

2I

2P

36

3D

3K

41

48

4F

4M

53

5A

5H

5O

65

6C

6J

70

8

G

O

16

1E

1M

24

2C

2K

32

3A

3I

40

48

4G

4O

56

5E

5M

64

6C

6K

72

7A

7I

80

9

I

11

1A

1J

22

2B

2K

33

3C

3L

44

4D

4M

55

5E

5N

66

6F

6O

77

7G

7P

88

8H

90

A

K

14

1E

1O

28

2I

32

3C

3M

46

4G

50

5A

5K

64

6E

6O

78

7I

82

8C

8M

96

9G

A0

B

M

17

1I

23

2E

2P

3A

3L

46

4H

52

5D

5O

69

6K

75

7G

81

8C

8N

98

9J

A4

AF

B0

C

O

1A

1M

28

2K

36

3I

44

4G

52

5E

60

6C

6O

7A

7M

88

8K

96

9I

A4

AG

B2

BE

C0

D

10

1D

20

2D

30

3D

40

4D

50

5D

60

6D

70

7D

80

8D

90

9D

A0

AD

B0

BD

C0

CD

D0

E

12

1G

24

2I

36

3K

48

4M

5A

5O

6C

70

7E

82

8G

94

9I

A6

AK

B8

BM

CA

CO

DC

E0

F

14

1J

28

2N

3C

41

4G

55

5K

69

6O

7D

82

8H

96

9L

AA

AP

BE

C3

CI

D7

DM

EB

F0

G

16

1M

2C

32

3I

48

4O

5E

64

6K

7A

80

8G

96

9M

AC

B2

BI

C8

CO

DE

E4

EK

FA

G0

H

18

1P

2G

37

3O

4F

56

5N

6E

75

7M

8D

94

9L

AC

B3

BK

CB

D2

DJ

EA

F1

FI

G9

H0

I

1A

22

2K

3C

44

4M

5E

66

6O

7G

88

90

9I

AA

B2

BK

CC

D4

DM

EE

F6

FO

GG

H8

I0

J

1C

25

2O

3H

4A

53

5M

6F

78

81

8K

9D

A6

AP

BI

CB

D4

DN

EG

F9

G2

GL

HE

I7

J0

K

1E

28

32

3M

4G

5A

64

6O

7I

8C

96

A0

AK

BE

C8

D2

DM

EG

FA

G4

GO

HI

IC

J6

K0

L

1G

2B

36

41

4M

5H

6C

77

82

8N

9I

AD

B8

C3

CO

DJ

EE

F9

G4

GP

HK

IF

JA

K5

L0

M

1I

2E

3A

46

52

5O

6K

7G

8C

98

A4

B0

BM

CI

DE

EA

F6

G2

GO

HK

IG

JC

K8

L4

M0

N

1K

2H

3E

4B

58

65

72

7P

8M

9J

AG

BD

CA

D7

E4

F1

FO

GL

HI

IF

JC

K9

L6

M3

N0

O

1M

2K

3I

4G

5E

6C

7A

88

96

A4

B2

C0

CO

DM

EK

FI

GG

HE

IC

JA

K8

L6

M4

N2

O0

P

1O

2N

3M

4L

5K

6J

7I

8H

9G

AF

BE

CD

DC

EB

FA

G9

H8

I7

J6

K5

L4

M3

N2

O1

P0

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

100

In base 27:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

11

13

15

17

19

1B

1D

1F

1H

1J

1L

1N

1P

3

6

9

C

F

I

L

O

10

13

16

19

1C

1F

1I

1L

1O

20

23

26

29

2C

2F

2I

2L

2O

4

8

C

G

K

O

11

15

19

1D

1H

1L

1P

22

26

2A

2E

2I

2M

2Q

33

37

3B

3F

3J

3N

5

A

F

K

P

13

18

1D

1I

1N

21

26

2B

2G

2L

2Q

34

39

3E

3J

3O

42

47

4C

4H

4M

6

C

I

O

13

19

1F

1L

20

26

2C

2I

2O

33

39

3F

3L

40

46

4C

4I

4O

53

59

5F

5L

7

E

L

11

18

1F

1M

22

29

2G

2N

33

3A

3H

3O

44

4B

4I

4P

55

5C

5J

5Q

66

6D

6K

8

G

O

15

1D

1L

22

2A

2I

2Q

37

3F

3N

44

4C

4K

51

59

5H

5P

66

6E

6M

73

7B

7J

9

I

10

19

1I

20

29

2I

30

39

3I

40

49

4I

50

59

5I

60

69

6I

70

79

7I

80

89

8I

A

K

13

1D

1N

26

2G

2Q

39

3J

42

4C

4M

55

5F

5P

68

6I

71

7B

7L

84

8E

8O

97

9H

B

M

16

1H

21

2C

2N

37

3I

42

4D

4O

58

5J

63

6E

6P

79

7K

84

8F

8Q

9A

9L

A5

AG

C

O

19

1L

26

2I

33

3F

40

4C

4O

59

5L

66

6I

73

7F

80

8C

8O

99

9L

A6

AI

B3

BF

D

Q

1C

1P

2B

2O

3A

3N

49

4M

58

5L

67

6K

76

7J

85

8I

94

9H

A3

AG

B2

BF

C1

CE

E

11

1F

22

2G

33

3H

44

4I

55

5J

66

6K

77

7L

88

8M

99

9N

AA

AO

BB

BP

CC

CQ

DD

F

13

1I

26

2L

39

3O

4C

50

5F

63

6I

76

7L

89

8O

9C

A0

AF

B3

BI

C6

CL

D9

DO

EC

G

15

1L

2A

2Q

3F

44

4K

59

5P

6E

73

7J

88

8O

9D

A2

AI

B7

BN

CC

D1

DH

E6

EM

FB

H

17

1O

2E

34

3L

4B

51

5I

68

6P

7F

85

8M

9C

A2

AJ

B9

BQ

CG

D6

DN

ED

F3

FK

GA

I

19

20

2I

39

40

4I

59

60

6I

79

80

8I

99

A0

AI

B9

C0

CI

D9

E0

EI

F9

G0

GI

H9

J

1B

23

2M

3E

46

4P

5H

69

71

7K

8C

94

9N

AF

B7

BQ

CI

DA

E2

EL

FD

G5

GO

HG

I8

K

1D

26

2Q

3J

4C

55

5P

6I

7B

84

8O

9H

AA

B3

BN

CG

D9

E2

EM

FF

G8

H1

HL

IE

J7

L

1F

29

33

3O

4I

5C

66

70

7L

8F

99

A3

AO

BI

CC

D6

E0

EL

FF

G9

H3

HO

II

JC

K6

M

1H

2C

37

42

4O

5J

6E

79

84

8Q

9L

AG

BB

C6

D1

DN

EI

FD

G8

H3

HP

IK

JF

KA

L5

N

1J

2F

3B

47

53

5Q

6M

7I

8E

9A

A6

B2

BP

CL

DH

ED

F9

G5

H1

HO

IK

JG

KC

L8

M4

O

1L

2I

3F

4C

59

66

73

80

8O

9L

AI

BF

CC

D9

E6

F3

G0

GO

HL

II

JF

KC

L9

M6

N3

P

1N

2L

3J

4H

5F

6D

7B

89

97

A5

B3

C1

CQ

DO

EM

FK

GI

HG

IE

JC

KA

L8

M6

N4

O2

Q

1P

2O

3N

4M

5L

6K

7J

8I

9H

AG

BF

CE

DD

EC

FB

GA

H9

I8

J7

K6

L5

M4

N3

O2

P1

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 28:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

10

12

14

16

18

1A

1C

1E

1G

1I

1K

1M

1O

3

6

9

C

F

I

L

O

R

12

15

18

1B

1E

1H

1K

1N

1Q

21

24

27

2A

2D

2G

2J

2M

4

8

C

G

K

O

10

14

18

1C

1G

1K

1O

20

24

28

2C

2G

2K

2O

30

34

38

3C

3G

3K

5

A

F

K

P

12

17

1C

1H

1M

1R

24

29

2E

2J

2O

31

36

3B

3G

3L

3Q

43

48

4D

4I

6

C

I

O

12

18

1E

1K

1Q

24

2A

2G

2M

30

36

3C

3I

3O

42

48

4E

4K

4Q

54

5A

5G

7

E

L

10

17

1E

1L

20

27

2E

2L

30

37

3E

3L

40

47

4E

4L

50

57

5E

5L

60

67

6E

8

G

O

14

1C

1K

20

28

2G

2O

34

3C

3K

40

48

4G

4O

54

5C

5K

60

68

6G

6O

74

7C

9

I

R

18

1H

1Q

27

2G

2P

36

3F

3O

45

4E

4N

54

5D

5M

63

6C

6L

72

7B

7K

81

8A

A

K

12

1C

1M

24

2E

2O

36

3G

3Q

48

4I

50

5A

5K

62

6C

6M

74

7E

7O

86

8G

8Q

98

B

M

15

1G

1R

2A

2L

34

3F

3Q

49

4K

53

5E

5P

68

6J

72

7D

7O

87

8I

91

9C

9N

A6

C

O

18

1K

24

2G

30

3C

3O

48

4K

54

5G

60

6C

6O

78

7K

84

8G

90

9C

9O

A8

AK

B4

D

Q

1B

1O

29

2M

37

3K

45

4I

53

5G

61

6E

6R

7C

7P

8A

8N

98

9L

A6

AJ

B4

BH

C2

E

10

1E

20

2E

30

3E

40

4E

50

5E

60

6E

70

7E

80

8E

90

9E

A0

AE

B0

BE

C0

CE

D0

F

12

1H

24

2J

36

3L

48

4N

5A

5P

6C

6R

7E

81

8G

93

9I

A5

AK

B7

BM

C9

CO

DB

DQ

G

14

1K

28

2O

3C

40

4G

54

5K

68

6O

7C

80

8G

94

9K

A8

AO

BC

C0

CG

D4

DK

E8

EO

H

16

1N

2C

31

3I

47

4O

5D

62

6J

78

7P

8E

93

9K

A9

AQ

BF

C4

CL

DA

DR

EG

F5

FM

I

18

1Q

2G

36

3O

4E

54

5M

6C

72

7K

8A

90

9I

A8

AQ

BG

C6

CO

DE

E4

EM

FC

G2

GK

J

1A

21

2K

3B

42

4L

5C

63

6M

7D

84

8N

9E

A5

AO

BF

C6

CP

DG

E7

EQ

FH

G8

GR

HI

K

1C

24

2O

3G

48

50

5K

6C

74

7O

8G

98

A0

AK

BC

C4

CO

DG

E8

F0

FK

GC

H4

HO

IG

L

1E

27

30

3L

4E

57

60

6L

7E

87

90

9L

AE

B7

C0

CL

DE

E7

F0

FL

GE

H7

I0

IL

JE

M

1G

2A

34

3Q

4K

5E

68

72

7O

8I

9C

A6

B0

BM

CG

DA

E4

EQ

FK

GE

H8

I2

IO

JI

KC

N

1I

2D

38

43

4Q

5L

6G

7B

86

91

9O

AJ

BE

C9

D4

DR

EM

FH

GC

H7

I2

IP

JK

KF

LA

O

1K

2G

3C

48

54

60

6O

7K

8G

9C

A8

B4

C0

CO

DK

EG

FC

G8

H4

I0

IO

JK

KG

LC

M8

P

1M

2J

3G

4D

5A

67

74

81

8Q

9N

AK

BH

CE

DB

E8

F5

G2

GR

HO

IL

JI

KF

LC

M9

N6

Q

1O

2M

3K

4I

5G

6E

7C

8A

98

A6

B4

C2

D0

DQ

EO

FM

GK

HI

IG

JE

KC

LA

M8

N6

O4

R

1Q

2P

3O

4N

5M

6L

7K

8J

9I

AH

BG

CF

DE

ED

FC

GB

HA

I9

J8

K7

L6

M5

N4

O3

P2

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 29:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

11

13

15

17

19

1B

1D

1F

1H

1J

1L

1N

3

6

9

C

F

I

L

O

R

11

14

17

1A

1D

1G

1J

1M

1P

1S

22

25

28

2B

2E

2H

2K

4

8

C

G

K

O

S

13

17

1B

1F

1J

1N

1R

22

26

2A

2E

2I

2M

2Q

31

35

39

3D

3H

5

A

F

K

P

11

16

1B

1G

1L

1Q

22

27

2C

2H

2M

2R

33

38

3D

3I

3N

3S

44

49

4E

6

C

I

O

11

17

1D

1J

1P

22

28

2E

2K

2Q

33

39

3F

3L

3R

44

4A

4G

4M

4S

55

5B

7

E

L

S

16

1D

1K

1R

25

2C

2J

2Q

34

3B

3I

3P

43

4A

4H

4O

52

59

5G

5N

61

68

8

G

O

13

1B

1J

1R

26

2E

2M

31

39

3H

3P

44

4C

4K

4S

57

5F

5N

62

6A

6I

6Q

75

9

I

R

17

1G

1P

25

2E

2N

33

3C

3L

41

4A

4J

4S

58

5H

5Q

66

6F

6O

74

7D

7M

82

A

K

11

1B

1L

22

2C

2M

33

3D

3N

44

4E

4O

55

5F

5P

66

6G

6Q

77

7H

7R

88

8I

8S

B

M

14

1F

1Q

28

2J

31

3C

3N

45

4G

4R

59

5K

62

6D

6O

76

7H

7S

8A

8L

93

9E

9P

C

O

17

1J

22

2E

2Q

39

3L

44

4G

4S

5B

5N

66

6I

71

7D

7P

88

8K

93

9F

9R

AA

AM

D

Q

1A

1N

27

2K

34

3H

41

4E

4R

5B

5O

68

6L

75

7I

82

8F

8S

9C

9P

A9

AM

B6

BJ

E

S

1D

1R

2C

2Q

3B

3P

4A

4O

59

5N

68

6M

77

7L

86

8K

95

9J

A4

AI

B3

BH

C2

CG

F

11

1G

22

2H

33

3I

44

4J

55

5K

66

6L

77

7M

88

8N

99

9O

AA

AP

BB

BQ

CC

CR

DD

G

13

1J

26

2M

39

3P

4C

4S

5F

62

6I

75

7L

88

8O

9B

9R

AE

B1

BH

C4

CK

D7

DN

EA

H

15

1M

2A

2R

3F

43

4K

58

5P

6D

71

7I

86

8N

9B

9S

AG

B4

BL

C9

CQ

DE

E2

EJ

F7

I

17

1P

2E

33

3L

4A

4S

5H

66

6O

7D

82

8K

99

9R

AG

B5

BN

CC

D1

DJ

E8

EQ

FF

G4

J

19

1S

2I

38

3R

4H

57

5Q

6G

76

7P

8F

95

9O

AE

B4

BN

CD

D3

DM

EC

F2

FL

GB

H1

K

1B

22

2M

3D

44

4O

5F

66

6Q

7H

88

8S

9J

AA

B1

BL

CC

D3

DN

EE

F5

FP

GG

H7

HR

L

1D

25

2Q

3I

4A

52

5N

6F

77

7S

8K

9C

A4

AP

BH

C9

D1

DM

EE

F6

FR

GJ

HB

I3

IO

M

1F

28

31

3N

4G

59

62

6O

7H

8A

93

9P

AI

BB

C4

CQ

DJ

EC

F5

FR

GK

HD

I6

IS

JL

N

1H

2B

35

3S

4M

5G

6A

74

7R

8L

9F

A9

B3

BQ

CK

DE

E8

F2

FP

GJ

HD

I7

J1

JO

KI

O

1J

2E

39

44

4S

5N

6I

7D

88

93

9R

AM

BH

CC

D7

E2

EQ

FL

GG

HB

I6

J1

JP

KK

LF

P

1L

2H

3D

49

55

61

6Q

7M

8I

9E

AA

B6

C2

CR

DN

EJ

FF

GB

H7

I3

IS

JO

KK

LG

MC

Q

1N

2K

3H

4E

5B

68

75

82

8S

9P

AM

BJ

CG

DD

EA

F7

G4

H1

HR

IO

JL

KI

LF

MC

N9

R

1P

2N

3L

4J

5H

6F

7D

8B

99

A7

B5

C3

D1

DS

EQ

FO

GM

HK

II

JG

KE

LC

MA

N8

O6

S

1R

2Q

3P

4O

5N

6M

7L

8K

9J

AI

BH

CG

DF

EE

FD

GC

HB

IA

J9

K8

L7

M6

N5

O4

P3

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 30:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

10

12

14

16

18

1A

1C

1E

1G

1I

1K

1M

3

6

9

C

F

I

L

O

R

10

13

16

19

1C

1F

1I

1L

1O

1R

20

23

26

29

2C

2F

2I

4

8

C

G

K

O

S

12

16

1A

1E

1I

1M

1Q

20

24

28

2C

2G

2K

2O

2S

32

36

3A

3E

5

A

F

K

P

10

15

1A

1F

1K

1P

20

25

2A

2F

2K

2P

30

35

3A

3F

3K

3P

40

45

4A

6

C

I

O

10

16

1C

1I

1O

20

26

2C

2I

2O

30

36

3C

3I

3O

40

46

4C

4I

4O

50

56

7

E

L

S

15

1C

1J

1Q

23

2A

2H

2O

31

38

3F

3M

3T

46

4D

4K

4R

54

5B

5I

5P

62

8

G

O

12

1A

1I

1Q

24

2C

2K

2S

36

3E

3M

40

48

4G

4O

52

5A

5I

5Q

64

6C

6K

6S

9

I

R

16

1F

1O

23

2C

2L

30

39

3I

3R

46

4F

4O

53

5C

5L

60

69

6I

6R

76

7F

7O

A

K

10

1A

1K

20

2A

2K

30

3A

3K

40

4A

4K

50

5A

5K

60

6A

6K

70

7A

7K

80

8A

8K

B

M

13

1E

1P

26

2H

2S

39

3K

41

4C

4N

54

5F

5Q

67

6I

6T

7A

7L

82

8D

8O

95

9G

C

O

16

1I

20

2C

2O

36

3I

40

4C

4O

56

5I

60

6C

6O

76

7I

80

8C

8O

96

9I

A0

AC

D

Q

19

1M

25

2I

31

3E

3R

4A

4N

56

5J

62

6F

6S

7B

7O

87

8K

93

9G

9T

AC

AP

B8

E

S

1C

1Q

2A

2O

38

3M

46

4K

54

5I

62

6G

70

7E

7S

8C

8Q

9A

9O

A8

AM

B6

BK

C4

F

10

1F

20

2F

30

3F

40

4F

50

5F

60

6F

70

7F

80

8F

90

9F

A0

AF

B0

BF

C0

CF

D0

G

12

1I

24

2K

36

3M

48

4O

5A

5Q

6C

6S

7E

80

8G

92

9I

A4

AK

B6

BM

C8

CO

DA

DQ

H

14

1L

28

2P

3C

3T

4G

53

5K

67

6O

7B

7S

8F

92

9J

A6

AN

BA

BR

CE

D1

DI

E5

EM

I

16

1O

2C

30

3I

46

4O

5C

60

6I

76

7O

8C

90

9I

A6

AO

BC

C0

CI

D6

DO

EC

F0

FI

J

18

1R

2G

35

3O

4D

52

5L

6A

6T

7I

87

8Q

9F

A4

AN

BC

C1

CK

D9

DS

EH

F6

FP

GE

K

1A

20

2K

3A

40

4K

5A

60

6K

7A

80

8K

9A

A0

AK

BA

C0

CK

DA

E0

EK

FA

G0

GK

HA

L

1C

23

2O

3F

46

4R

5I

69

70

7L

8C

93

9O

AF

B6

BR

CI

D9

E0

EL

FC

G3

GO

HF

I6

M

1E

26

2S

3K

4C

54

5Q

6I

7A

82

8O

9G

A8

B0

BM

CE

D6

DS

EK

FC

G4

GQ

HI

IA

J2

N

1G

29

32

3P

4I

5B

64

6R

7K

8D

96

9T

AM

BF

C8

D1

DO

EH

FA

G3

GQ

HJ

IC

J5

JS

O

1I

2C

36

40

4O

5I

6C

76

80

8O

9I

AC

B6

C0

CO

DI

EC

F6

G0

GO

HI

IC

J6

K0

KO

P

1K

2F

3A

45

50

5P

6K

7F

8A

95

A0

AP

BK

CF

DA

E5

F0

FP

GK

HF

IA

J5

K0

KP

LK

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1M

2I

3E

4A

56

62

6S

7O

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AC

B8

C4

D0

DQ

EM

FI

GE

HA

I6

J2

JS

KO

LK

MG

R

1O

2L

3I

4F

5C

69

76

83

90

9R

AO

BL

CI

DF

EC

F9

G6

H3

I0

IR

JO

KL

LI

MF

NC

S

1Q

2O

3M

4K

5I

6G

7E

8C

9A

A8

B6

C4

D2

E0

ES

FQ

GO

HM

IK

JI

KG

LE

MC

NA

O8

T

1S

2R

3Q

4P

5O

6N

7M

8L

9K

AJ

BI

CH

DG

EF

FE

GD

HC

IB

JA

K9

L8

M7

N6

O5

P4

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 31:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

11

13

15

17

19

1B

1D

1F

1H

1J

1L

3

6

9

C

F

I

L

O

R

U

12

15

18

1B

1E

1H

1K

1N

1Q

1T

21

24

27

2A

2D

2G

4

8

C

G

K

O

S

11

15

19

1D

1H

1L

1P

1T

22

26

2A

2E

2I

2M

2Q

2U

33

37

3B

5

A

F

K

P

U

14

19

1E

1J

1O

1T

23

28

2D

2I

2N

2S

32

37

3C

3H

3M

3R

41

46

6

C

I

O

U

15

1B

1H

1N

1T

24

2A

2G

2M

2S

33

39

3F

3L

3R

42

48

4E

4K

4Q

51

7

E

L

S

14

1B

1I

1P

21

28

2F

2M

2T

35

3C

3J

3Q

42

49

4G

4N

4U

56

5D

5K

5R

8

G

O

11

19

1H

1P

22

2A

2I

2Q

33

3B

3J

3R

44

4C

4K

4S

55

5D

5L

5T

66

6E

6M

9

I

R

15

1E

1N

21

2A

2J

2S

36

3F

3O

42

4B

4K

4T

57

5G

5P

63

6C

6L

6U

78

7H

A

K

U

19

1J

1T

28

2I

2S

37

3H

3R

46

4G

4Q

55

5F

5P

64

6E

6O

73

7D

7N

82

8C

B

M

12

1D

1O

24

2F

2Q

36

3H

3S

48

4J

4U

5A

5L

61

6C

6N

73

7E

7P

85

8G

8R

97

C

O

15

1H

1T

2A

2M

33

3F

3R

48

4K

51

5D

5P

66

6I

6U

7B

7N

84

8G

8S

99

9L

A2

D

Q

18

1L

23

2G

2T

3B

3O

46

4J

51

5E

5R

69

6M

74

7H

7U

8C

8P

97

9K

A2

AF

AS

E

S

1B

1P

28

2M

35

3J

42

4G

4U

5D

5R

6A

6O

77

7L

84

8I

91

9F

9T

AC

AQ

B9

BN

F

U

1E

1T

2D

2S

3C

3R

4B

4Q

5A

5P

69

6O

78

7N

87

8M

96

9L

A5

AK

B4

BJ

C3

CI

G

11

1H

22

2I

33

3J

44

4K

55

5L

66

6M

77

7N

88

8O

99

9P

AA

AQ

BB

BR

CC

CS

DD

H

13

1K

26

2N

39

3Q

4C

4T

5F

61

6I

74

7L

87

8O

9A

9R

AD

AU

BG

C2

CJ

D5

DM

E8

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15

1N

2A

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3F

42

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57

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6C

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7H

84

8M

99

9R

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B1

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C6

CO

DB

DT

EG

F3

J

17

1Q

2E

32

3L

49

4S

5G

64

6N

7B

7U

8I

96

9P

AD

B1

BK

C8

CR

DF

E3

EM

FA

FT

K

19

1T

2I

37

3R

4G

55

5P

6E

73

7N

8C

91

9L

AA

AU

BJ

C8

CS

DH

E6

EQ

FF

G4

GO

L

1B

21

2M

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42

4N

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63

6O

7E

84

8P

9F

A5

AQ

BG

C6

CR

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E7

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G8

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HJ

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24

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48

4U

5L

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73

7P

8G

97

9T

AK

BB

C2

CO

DF

E6

ES

FJ

GA

H1

HN

IE

N

1F

27

2U

3M

4E

56

5T

6L

7D

85

8S

9K

AC

B4

BR

CJ

DB

E3

EQ

FI

GA

H2

HP

IH

J9

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1H

2A

33

3R

4K

5D

66

6U

7N

8G

99

A2

AQ

BJ

CC

D5

DT

EM

FF

G8

H1

HP

II

JB

K4

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1J

2D

37

41

4Q

5K

6E

78

82

8R

9L

AF

B9

C3

CS

DM

EG

FA

G4

GT

HN

IH

JB

K5

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1L

2G

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46

51

5R

6M

7H

8C

97

A2

AS

BN

CI

DD

E8

F3

FT

GO

HJ

IE

J9

K4

KU

LP

R

1N

2J

3F

4B

57

63

6U

7Q

8M

9I

AE

BA

C6

D2

DT

EP

FL

GH

HD

I9

J5

K1

KS

LO

MK

S

1P

2M

3J

4G

5D

6A

77

84

91

9T

AQ

BN

CK

DH

EE

FB

G8

H5

I2

IU

JR

KO

LL

MI

NF

T

1R

2P

3N

4L

5J

6H

7F

8D

9B

A9

B7

C5

D3

E1

EU

FS

GQ

HO

IM

JK

KI

LG

ME

NC

OA

U

1T

2S

3R

4Q

5P

6O

7N

8M

9L

AK

BJ

CI

DH

EG

FF

GE

HD

IC

JB

KA

L9

M8

N7

O6

P5

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 32:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

10

12

14

16

18

1A

1C

1E

1G

1I

1K

3

6

9

C

F

I

L

O

R

U

11

14

17

1A

1D

1G

1J

1M

1P

1S

1V

22

25

28

2B

2E

4

8

C

G

K

O

S

10

14

18

1C

1G

1K

1O

1S

20

24

28

2C

2G

2K

2O

2S

30

34

38

5

A

F

K

P

U

13

18

1D

1I

1N

1S

21

26

2B

2G

2L

2Q

2V

34

39

3E

3J

3O

3T

42

6

C

I

O

U

14

1A

1G

1M

1S

22

28

2E

2K

2Q

30

36

3C

3I

3O

3U

44

4A

4G

4M

4S

7

E

L

S

13

1A

1H

1O

1V

26

2D

2K

2R

32

39

3G

3N

3U

45

4C

4J

4Q

51

58

5F

5M

8

G

O

10

18

1G

1O

20

28

2G

2O

30

38

3G

3O

40

48

4G

4O

50

58

5G

5O

60

68

6G

9

I

R

14

1D

1M

1V

28

2H

2Q

33

3C

3L

3U

47

4G

4P

52

5B

5K

5T

66

6F

6O

71

7A

A

K

U

18

1I

1S

26

2G

2Q

34

3E

3O

42

4C

4M

50

5A

5K

5U

68

6I

6S

76

7G

7Q

84

B

M

11

1C

1N

22

2D

2O

33

3E

3P

44

4F

4Q

55

5G

5R

66

6H

6S

77

7I

7T

88

8J

8U

C

O

14

1G

1S

28

2K

30

3C

3O

44

4G

4S

58

5K

60

6C

6O

74

7G

7S

88

8K

90

9C

9O

D

Q

17

1K

21

2E

2R

38

3L

42

4F

4S

59

5M

63

6G

6T

7A

7N

84

8H

8U

9B

9O

A5

AI

E

S

1A

1O

26

2K

32

3G

3U

4C

4Q

58

5M

64

6I

70

7E

7S

8A

8O

96

9K

A2

AG

AU

BC

F

U

1D

1S

2B

2Q

39

3O

47

4M

55

5K

63

6I

71

7G

7V

8E

8T

9C

9R

AA

AP

B8

BN

C6

G

10

1G

20

2G

30

3G

40

4G

50

5G

60

6G

70

7G

80

8G

90

9G

A0

AG

B0

BG

C0

CG

D0

H

12

1J

24

2L

36

3N

48

4P

5A

5R

6C

6T

7E

7V

8G

91

9I

A3

AK

B5

BM

C7

CO

D9

DQ

I

14

1M

28

2Q

3C

3U

4G

52

5K

66

6O

7A

7S

8E

90

9I

A4

AM

B8

BQ

CC

CU

DG

E2

EK

J

16

1P

2C

2V

3I

45

4O

5B

5U

6H

74

7N

8A

8T

9G

A3

AM

B9

BS

CF

D2

DL

E8

ER

FE

K

18

1S

2G

34

3O

4C

50

5K

68

6S

7G

84

8O

9C

A0

AK

B8

BS

CG

D4

DO

EC

F0

FK

G8

L

1A

1V

2K

39

3U

4J

58

5T

6I

77

7S

8H

96

9R

AG

B5

BQ

CF

D4

DP

EE

F3

FO

GD

H2

M

1C

22

2O

3E

44

4Q

5G

66

6S

7I

88

8U

9K

AA

B0

BM

CC

D2

DO

EE

F4

FQ

GG

H6

HS

N

1E

25

2S

3J

4A

51

5O

6F

76

7T

8K

9B

A2

AP

BG

C7

CU

DL

EC

F3

FQ

GH

H8

HV

IM

O

1G

28

30

3O

4G

58

60

6O

7G

88

90

9O

AG

B8

C0

CO

DG

E8

F0

FO

GG

H8

I0

IO

JG

P

1I

2B

34

3T

4M

5F

68

71

7Q

8J

9C

A5

AU

BN

CG

D9

E2

ER

FK

GD

H6

HV

IO

JH

KA

Q

1K

2E

38

42

4S

5M

6G

7A

84

8U

9O

AI

BC

C6

D0

DQ

EK

FE

G8

H2

HS

IM

JG

KA

L4

R

1M

2H

3C

47

52

5T

6O

7J

8E

99

A4

AV

BQ

CL

DG

EB

F6

G1

GS

HN

II

JD

K8

L3

LU

S

1O

2K

3G

4C

58

64

70

7S

8O

9K

AG

BC

C8

D4

E0

ES

FO

GK

HG

IC

J8

K4

L0

LS

MO

T

1Q

2N

3K

4H

5E

6B

78

85

92

9V

AS

BP

CM

DJ

EG

FD

GA

H7

I4

J1

JU

KR

LO

ML

NI

U

1S

2Q

3O

4M

5K

6I

7G

8E

9C

AA

B8

C6

D4

E2

F0

FU

GS

HQ

IO

JM

KK

LI

MG

NE

OC

V

1U

2T

3S

4R

5Q

6P

7O

8N

9M

AL

BK

CJ

DI

EH

FG

GF

HE

ID

JC

KB

LA

M9

N8

O7

P6

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 33:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

W

11

13

15

17

19

1B

1D

1F

1H

1J

3

6

9

C

F

I

L

O

R

U

10

13

16

19

1C

1F

1I

1L

1O

1R

1U

20

23

26

29

2C

4

8

C

G

K

O

S

W

13

17

1B

1F

1J

1N

1R

1V

22

26

2A

2E

2I

2M

2Q

2U

31

35

5

A

F

K

P

U

12

17

1C

1H

1M

1R

1W

24

29

2E

2J

2O

2T

31

36

3B

3G

3L

3Q

3V

6

C

I

O

U

13

19

1F

1L

1R

20

26

2C

2I

2O

2U

33

39

3F

3L

3R

40

46

4C

4I

4O

7

E

L

S

12

19

1G

1N

1U

24

2B

2I

2P

2W

36

3D

3K

3R

41

48

4F

4M

4T

53

5A

5H

8

G

O

W

17

1F

1N

1V

26

2E

2M

2U

35

3D

3L

3T

44

4C

4K

4S

53

5B

5J

5R

62

6A

9

I

R

13

1C

1L

1U

26

2F

2O

30

39

3I

3R

43

4C

4L

4U

56

5F

5O

60

69

6I

6R

73

A

K

U

17

1H

1R

24

2E

2O

31

3B

3L

3V

48

4I

4S

55

5F

5P

62

6C

6M

6W

79

7J

7T

B

M

10

1B

1M

20

2B

2M

30

3B

3M

40

4B

4M

50

5B

5M

60

6B

6M

70

7B

7M

80

8B

8M

C

O

13

1F

1R

26

2I

2U

39

3L

40

4C

4O

53

5F

5R

66

6I

6U

79

7L

80

8C

8O

93

9F

D

Q

16

1J

1W

2C

2P

35

3I

3V

4B

4O

54

5H

5U

6A

6N

73

7G

7T

89

8M

92

9F

9S

A8

E

S

19

1N

24

2I

2W

3D

3R

48

4M

53

5H

5V

6C

6Q

77

7L

82

8G

8U

9B

9P

A6

AK

B1

F

U

1C

1R

29

2O

36

3L

43

4I

50

5F

5U

6C

6R

79

7O

86

8L

93

9I

A0

AF

AU

BC

BR

G

W

1F

1V

2E

2U

3D

3T

4C

4S

5B

5R

6A

6Q

79

7P

88

8O

97

9N

A6

AM

B5

BL

C4

CK

H

11

1I

22

2J

33

3K

44

4L

55

5M

66

6N

77

7O

88

8P

99

9Q

AA

AR

BB

BS

CC

CT

DD

I

13

1L

26

2O

39

3R

4C

4U

5F

60

6I

73

7L

86

8O

99

9R

AC

AU

BF

C0

CI

D3

DL

E6

J

15

1O

2A

2T

3F

41

4K

56

5P

6B

6U

7G

82

8L

97

9Q

AC

AV

BH

C3

CM

D8

DR

ED

EW

K

17

1R

2E

31

3L

48

4S

5F

62

6M

79

7T

8G

93

9N

AA

AU

BH

C4

CO

DB

DV

EI

F5

FP

L

19

1U

2I

36

3R

4F

53

5O

6C

70

7L

89

8U

9I

A6

AR

BF

C3

CO

DC

E0

EL

F9

FU

GI

M

1B

20

2M

3B

40

4M

5B

60

6M

7B

80

8M

9B

A0

AM

BB

C0

CM

DB

E0

EM

FB

G0

GM

HB

N

1D

23

2Q

3G

46

4T

5J

69

6W

7M

8C

92

9P

AF

B5

BS

CI

D8

DV

EL

FB

G1

GO

HE

I4

O

1F

26

2U

3L

4C

53

5R

6I

79

80

8O

9F

A6

AU

BL

CC

D3

DR

EI

F9

G0

GO

HF

I6

IU

P

1H

29

31

3Q

4I

5A

62

6R

7J

8B

93

9S

AK

BC

C4

CT

DL

ED

F5

FU

GM

HE

I6

IV

JN

Q

1J

2C

35

3V

4O

5H

6A

73

7T

8M

9F

A8

B1

BR

CK

DD

E6

EW

FP

GI

HB

I4

IU

JN

KG

R

1L

2F

39

43

4U

5O

6I

7C

86

90

9R

AL

BF

C9

D3

DU

EO

FI

GC

H6

I0

IR

JL

KF

L9

S

1N

2I

3D

48

53

5V

6Q

7L

8G

9B

A6

B1

BT

CO

DJ

EE

F9

G4

GW

HR

IM

JH

KC

L7

M2

T

1P

2L

3H

4D

59

65

71

7U

8Q

9M

AI

BE

CA

D6

E2

EV

FR

GN

HJ

IF

JB

K7

L3

LW

MS

U

1R

2O

3L

4I

5F

6C

79

86

93

A0

AU

BR

CO

DL

EI

FF

GC

H9

I6

J3

K0

KU

LR

MO

NL

V

1T

2R

3P

4N

5L

6J

7H

8F

9D

AB

B9

C7

D5

E3

F1

FW

GU

HS

IQ

JO

KM

LK

MI

NG

OE

W

1V

2U

3T

4S

5R

6Q

7P

8O

9N

AM

BL

CK

DJ

EI

FH

GG

HF

IE

JD

KC

LB

MA

N9

O8

P7

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 34:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

W

10

12

14

16

18

1A

1C

1E

1G

1I

3

6

9

C

F

I

L

O

R

U

X

12

15

18

1B

1E

1H

1K

1N

1Q

1T

1W

21

24

27

2A

4

8

C

G

K

O

S

W

12

16

1A

1E

1I

1M

1Q

1U

20

24

28

2C

2G

2K

2O

2S

2W

32

5

A

F

K

P

U

11

16

1B

1G

1L

1Q

1V

22

27

2C

2H

2M

2R

2W

33

38

3D

3I

3N

3S

6

C

I

O

U

12

18

1E

1K

1Q

1W

24

2A

2G

2M

2S

30

36

3C

3I

3O

3U

42

48

4E

4K

7

E

L

S

11

18

1F

1M

1T

22

29

2G

2N

2U

33

3A

3H

3O

3V

44

4B

4I

4P

4W

55

5C

8

G

O

W

16

1E

1M

1U

24

2C

2K

2S

32

3A

3I

3Q

40

48

4G

4O

4W

56

5E

5M

5U

64

9

I

R

12

1B

1K

1T

24

2D

2M

2V

36

3F

3O

3X

48

4H

4Q

51

5A

5J

5S

63

6C

6L

6U

A

K

U

16

1G

1Q

22

2C

2M

2W

38

3I

3S

44

4E

4O

50

5A

5K

5U

66

6G

6Q

72

7C

7M

B

M

X

1A

1L

1W

29

2K

2V

38

3J

3U

47

4I

4T

56

5H

5S

65

6G

6R

74

7F

7Q

83

8E

C

O

12

1E

1Q

24

2G

2S

36

3I

3U

48

4K

4W

5A

5M

60

6C

6O

72

7E

7Q

84

8G

8S

96

D

Q

15

1I

1V

2A

2N

32

3F

3S

47

4K

4X

5C

5P

64

6H

6U

79

7M

81

8E

8R

96

9J

9W

E

S

18

1M

22

2G

2U

3A

3O

44

4I

4W

5C

5Q

66

6K

70

7E

7S

88

8M

92

9G

9U

AA

AO

F

U

1B

1Q

27

2M

33

3I

3X

4E

4T

5A

5P

66

6L

72

7H

7W

8D

8S

99

9O

A5

AK

B1

BG

G

W

1E

1U

2C

2S

3A

3Q

48

4O

56

5M

64

6K

72

7I

80

8G

8W

9E

9U

AC

AS

BA

BQ

C8

H

10

1H

20

2H

30

3H

40

4H

50

5H

60

6H

70

7H

80

8H

90

9H

A0

AH

B0

BH

C0

CH

D0

I

12

1K

24

2M

36

3O

48

4Q

5A

5S

6C

6U

7E

7W

8G

90

9I

A2

AK

B4

BM

C6

CO

D8

DQ

J

14

1N

28

2R

3C

3V

4G

51

5K

65

6O

79

7S

8D

8W

9H

A2

AL

B6

BP

CA

CT

DE

DX

EI

K

16

1Q

2C

2W

3I

44

4O

5A

5U

6G

72

7M

88

8S

9E

A0

AK

B6

BQ

CC

CW

DI

E4

EO

FA

L

18

1T

2G

33

3O

4B

4W

5J

66

6R

7E

81

8M

99

9U

AH

B4

BP

CC

CX

DK

E7

ES

FF

G2

M

1A

1W

2K

38

3U

4I

56

5S

6G

74

7Q

8E

92

9O

AC

B0

BM

CA

CW

DK

E8

EU

FI

G6

GS

N

1C

21

2O

3D

42

4P

5E

63

6Q

7F

84

8R

9G

A5

AS

BH

C6

CT

DI

E7

EU

FJ

G8

GV

HK

O

1E

24

2S

3I

48

4W

5M

6C

72

7Q

8G

96

9U

AK

BA

C0

CO

DE

E4

ES

FI

G8

GW

HM

IC

P

1G

27

2W

3N

4E

55

5U

6L

7C

83

8S

9J

AA

B1

BQ

CH

D8

DX

EO

FF

G6

GV

HM

ID

J4

Q

1I

2A

32

3S

4K

5C

64

6U

7M

8E

96

9W

AO

BG

C8

D0

DQ

EI

FA

G2

GS

HK

IC

J4

JU

R

1K

2D

36

3X

4Q

5J

6C

75

7W

8P

9I

AB

B4

BV

CO

DH

EA

F3

FU

GN

HG

I9

J2

JT

KM

S

1M

2G

3A

44

4W

5Q

6K

7E

88

92

9U

AO

BI

CC

D6

E0

ES

FM

GG

HA

I4

IW

JQ

KK

LE

T

1O

2J

3E

49

54

5X

6S

7N

8I

9D

A8

B3

BW

CR

DM

EH

FC

G7

H2

HV

IQ

JL

KG

LB

M6

U

1Q

2M

3I

4E

5A

66

72

7W

8S

9O

AK

BG

CC

D8

E4

F0

FU

GQ

HM

II

JE

KA

L6

M2

MW

V

1S

2P

3M

4J

5G

6D

7A

87

94

A1

AW

BT

CQ

DN

EK

FH

GE

HB

I8

J5

K2

KX

LU

MR

NO

W

1U

2S

3Q

4O

5M

6K

7I

8G

9E

AC

BA

C8

D6

E4

F2

G0

GW

HU

IS

JQ

KO

LM

MK

NI

OG

X

1W

2V

3U

4T

5S

6R

7Q

8P

9O

AN

BM

CL

DK

EJ

FI

GH

HG

IF

JE

KD

LC

MB

NA

O9

P8

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 35:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

W

Y

11

13

15

17

19

1B

1D

1F

1H

3

6

9

C

F

I

L

O

R

U

X

11

14

17

1A

1D

1G

1J

1M

1P

1S

1V

1Y

22

25

28

4

8

C

G

K

O

S

W

11

15

19

1D

1H

1L

1P

1T

1X

22

26

2A

2E

2I

2M

2Q

2U

2Y

5

A

F

K

P

U

10

15

1A

1F

1K

1P

1U

20

25

2A

2F

2K

2P

2U

30

35

3A

3F

3K

3P

6

C

I

O

U

11

17

1D

1J

1P

1V

22

28

2E

2K

2Q

2W

33

39

3F

3L

3R

3X

44

4A

4G

7

E

L

S

10

17

1E

1L

1S

20

27

2E

2L

2S

30

37

3E

3L

3S

40

47

4E

4L

4S

50

57

8

G

O

W

15

1D

1L

1T

22

2A

2I

2Q

2Y

37

3F

3N

3V

44

4C

4K

4S

51

59

5H

5P

5X

9

I

R

11

1A

1J

1S

22

2B

2K

2T

33

3C

3L

3U

44

4D

4M

4V

55

5E

5N

5W

66

6F

6O

A

K

U

15

1F

1P

20

2A

2K

2U

35

3F

3P

40

4A

4K

4U

55

5F

5P

60

6A

6K

6U

75

7F

B

M

X

19

1K

1V

27

2I

2T

35

3G

3R

43

4E

4P

51

5C

5N

5Y

6A

6L

6W

78

7J

7U

86

C

O

11

1D

1P

22

2E

2Q

33

3F

3R

44

4G

4S

55

5H

5T

66

6I

6U

77

7J

7V

88

8K

8W

D

Q

14

1H

1U

28

2L

2Y

3C

3P

43

4G

4T

57

5K

5X

6B

6O

72

7F

7S

86

8J

8W

9A

9N

E

S

17

1L

20

2E

2S

37

3L

40

4E

4S

57

5L

60

6E

6S

77

7L

80

8E

8S

97

9L

A0

AE

F

U

1A

1P

25

2K

30

3F

3U

4A

4P

55

5K

60

6F

6U

7A

7P

85

8K

90

9F

9U

AA

AP

B5

G

W

1D

1T

2A

2Q

37

3N

44

4K

51

5H

5X

6E

6U

7B

7R

88

8O

95

9L

A2

AI

AY

BF

BV

H

Y

1G

1X

2F

2W

3E

3V

4D

4U

5C

5T

6B

6S

7A

7R

89

8Q

98

9P

A7

AO

B6

BN

C5

CM

I

11

1J

22

2K

33

3L

44

4M

55

5N

66

6O

77

7P

88

8Q

99

9R

AA

AS

BB

BT

CC

CU

DD

J

13

1M

26

2P

39

3S

4C

4V

5F

5Y

6I

72

7L

85

8O

98

9R

AB

AU

BE

BX

CH

D1

DK

E4

K

15

1P

2A

2U

3F

40

4K

55

5P

6A

6U

7F

80

8K

95

9P

AA

AU

BF

C0

CK

D5

DP

EA

EU

L

17

1S

2E

30

3L

47

4S

5E

60

6L

77

7S

8E

90

9L

A7

AS

BE

C0

CL

D7

DS

EE

F0

FL

M

19

1V

2I

35

3R

4E

51

5N

6A

6W

7J

86

8S

9F

A2

AO

BB

BX

CK

D7

DT

EG

F3

FP

GC

N

1B

1Y

2M

3A

3X

4L

59

5W

6K

78

7V

8J

97

9U

AI

B6

BT

CH

D5

DS

EG

F4

FR

GF

H3

O

1D

22

2Q

3F

44

4S

5H

66

6U

7J

88

8W

9L

AA

AY

BN

CC

D1

DP

EE

F3

FR

GG

H5

HT

P

1F

25

2U

3K

4A

50

5P

6F

75

7U

8K

9A

A0

AP

BF

C5

CU

DK

EA

F0

FP

GF

H5

HU

IK

Q

1H

28

2Y

3P

4G

57

5X

6O

7F

86

8W

9N

AE

B5

BV

CM

DD

E4

EU

FL

GC

H3

HT

IK

JB

R

1J

2B

33

3U

4M

5E

66

6X

7P

8H

99

A1

AS

BK

CC

D4

DV

EN

FF

G7

GY

HQ

II

JA

K2

S

1L

2E

37

40

4S

5L

6E

77

80

8S

9L

AE

B7

C0

CS

DL

EE

F7

G0

GS

HL

IE

J7

K0

KS

T

1N

2H

3B

45

4Y

5S

6M

7G

8A

94

9X

AR

BL

CF

D9

E3

EW

FQ

GK

HE

I8

J2

JV

KP

LJ

U

1P

2K

3F

4A

55

60

6U

7P

8K

9F

AA

B5

C0

CU

DP

EK

FF

GA

H5

I0

IU

JP

KK

LF

MA

V

1R

2N

3J

4F

5B

67

73

7Y

8U

9Q

AM

BI

CE

DA

E6

F2

FX

GT

HP

IL

JH

KD

L9

M5

N1

W

1T

2Q

3N

4K

5H

6E

7B

88

95

A2

AY

BV

CS

DP

EM

FJ

GG

HD

IA

J7

K4

L1

LX

MU

NR

X

1V

2T

3R

4P

5N

6L

7J

8H

9F

AD

BB

C9

D7

E5

F3

G1

GY

HW

IU

JS

KQ

LO

MM

NK

OI

Y

1X

2W

3V

4U

5T

6S

7R

8Q

9P

AO

BN

CM

DL

EK

FJ

GI

HH

IG

JF

KE

LD

MC

NB

OA

P9

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

In base 36:

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

2

4

6

8

A

C

E

G

I

K

M

O

Q

S

U

W

Y

10

12

14

16

18

1A

1C

1E

1G

3

6

9

C

F

I

L

O

R

U

X

10

13

16

19

1C

1F

1I

1L

1O

1R

1U

1X

20

23

26

4

8

C

G

K

O

S

W

10

14

18

1C

1G

1K

1O

1S

1W

20

24

28

2C

2G

2K

2O

2S

2W

5

A

F

K

P

U

Z

14

19

1E

1J

1O

1T

1Y

23

28

2D

2I

2N

2S

2X

32

37

3C

3H

3M

6

C

I

O

U

10

16

1C

1I

1O

1U

20

26

2C

2I

2O

2U

30

36

3C

3I

3O

3U

40

46

4C

7

E

L

S

Z

16

1D

1K

1R

1Y

25

2C

2J

2Q

2X

34

3B

3I

3P

3W

43

4A

4H

4O

4V

52

8

G

O

W

14

1C

1K

1S

20

28

2G

2O

2W

34

3C

3K

3S

40

48

4G

4O

4W

54

5C

5K

5S

9

I

R

10

19

1I

1R

20

29

2I

2R

30

39

3I

3R

40

49

4I

4R

50

59

5I

5R

60

69

6I

A

K

U

14

1E

1O

1Y

28

2I

2S

32

3C

3M

3W

46

4G

4Q

50

5A

5K

5U

64

6E

6O

6Y

78

B

M

X

18

1J

1U

25

2G

2R

32

3D

3O

3Z

4A

4L

4W

57

5I

5T

64

6F

6Q

71

7C

7N

7Y

C

O

10

1C

1O

20

2C

2O

30

3C

3O

40

4C

4O

50

5C

5O

60

6C

6O

70

7C

7O

80

8C

8O

D

Q

13

1G

1T

26

2J

2W

39

3M

3Z

4C

4P

52

5F

5S

65

6I

6V

78

7L

7Y

8B

8O

91

9E

E

S

16

1K

1Y

2C

2Q

34

3I

3W

4A

4O

52

5G

5U

68

6M

70

7E

7S

86

8K

8Y

9C

9Q

A4

F

U

19

1O

23

2I

2X

3C

3R

46

4L

50

5F

5U

69

6O

73

7I

7X

8C

8R

96

9L

A0

AF

AU

G

W

1C

1S

28

2O

34

3K

40

4G

4W

5C

5S

68

6O

74

7K

80

8G

8W

9C

9S

A8

AO

B4

BK

H

Y

1F

1W

2D

2U

3B

3S

49

4Q

57

5O

65

6M

73

7K

81

8I

8Z

9G

9X

AE

AV

BC

BT

CA

I

10

1I

20

2I

30

3I

40

4I

50

5I

60

6I

70

7I

80

8I

90

9I

A0

AI

B0

BI

C0

CI

D0

J

12

1L

24

2N

36

3P

48

4R

5A

5T

6C

6V

7E

7X

8G

8Z

9I

A1

AK

B3

BM

C5

CO

D7

DQ

K

14

1O

28

2S

3C

3W

4G

50

5K

64

6O

78

7S

8C

8W

9G

A0

AK

B4

BO

C8

CS

DC

DW

EG

L

16

1R

2C

2X

3I

43

4O

59

5U

6F

70

7L

86

8R

9C

9X

AI

B3

BO

C9

CU

DF

E0

EL

F6

M

18

1U

2G

32

3O

4A

4W

5I

64

6Q

7C

7Y

8K

96

9S

AE

B0

BM

C8

CU

DG

E2

EO

FA

FW

N

1A

1X

2K

37

3U

4H

54

5R

6E

71

7O

8B

8Y

9L

A8

AV

BI

C5

CS

DF

E2

EP

FC

FZ

GM

O

1C

20

2O

3C

40

4O

5C

60

6O

7C

80

8O

9C

A0

AO

BC

C0

CO

DC

E0

EO

FC

G0

GO

HC

P

1E

23

2S

3H

46

4V

5K

69

6Y

7N

8C

91

9Q

AF

B4

BT

CI

D7

DW

EL

FA

FZ

GO

HD

I2

Q

1G

26

2W

3M

4C

52

5S

6I

78

7Y

8O

9E

A4

AU

BK

CA

D0

DQ

EG

F6

FW

GM

HC

I2

IS

R

1I

29

30

3R

4I

59

60

6R

7I

89

90

9R

AI

B9

C0

CR

DI

E9

F0

FR

GI

H9

I0

IR

JI

S

1K

2C

34

3W

4O

5G

68

70

7S

8K

9C

A4

AW

BO

CG

D8

E0

ES

FK

GC

H4

HW

IO

JG

K8

T

1M

2F

38

41

4U

5N

6G

79

82

8V

9O

AH

BA

C3

CW

DP

EI

FB

G4

GX

HQ

IJ

JC

K5

KY

U

1O

2I

3C

46

50

5U

6O

7I

8C

96

A0

AU

BO

CI

DC

E6

F0

FU

GO

HI

IC

J6

K0

KU

LO

V

1Q

2L

3G

4B

56

61

6W

7R

8M

9H

AC

B7

C2

CX

DS

EN

FI

GD

H8

I3

IY

JT

KO

LJ

ME

W

1S

2O

3K

4G

5C

68

74

80

8W

9S

AO

BK

CG

DC

E8

F4

G0

GW

HS

IO

JK

KG

LC

M8

N4

X

1U

2R

3O

4L

5I

6F

7C

89

96

A3

B0

BX

CU

DR

EO

FL

GI

HF

IC

J9

K6

L3

M0

MX

NU

Y

1W

2U

3S

4Q

5O

6M

7K

8I

9G

AE

BC

CA

D8

E6

F4

G2

H0

HY

IW

JU

KS

LQ

MO

NM

OK

Z

1Y

2X

3W

4V

5U

6T

7S

8R

9Q

AP

BO

CN

DM

EL

FK

GJ

HI

IH

JG

KF

LE

MD

NC

OB

PA

10

20

30

40

50

60

70

80

90

A0

B0

C0

D0

E0

F0

G0

H0

I0

J0

K0

L0

M0

N0

O0

P0

Q0

Common LISP

(defun multiplication-table (n)
	(loop with formatting = (format nil "~~&~~{~~~A,2R~~^ ~~}" n)
		  and range = (loop for x from 1 to n collect x)
		for x from 1 to n
		do (format t formatting 
				(mapcar #'(lambda (y) (* y x))
					range))))

[DeadHead]

I use Base 2 and Base 16 quite often when dealing with lower level computer programming. Sometimes, it is much faster for me to think in hex or binary, instead of having to convert everything to decimal, and at other times, it helps optimize the code.

I don't ever use other bases though (except for octal in school work) at all.

[Harrisonized]

Really though, I can't see anything but proper understanding of bases by doing this. What will it help you knowing base 3? Will you achieve something? :x

IDK. I was thinking maybe it'd allow you to think faster because you can then think on multiple levels.

[Orit]

I am with Harrisonized on this.
Ambassador's children sometimes spend so much time that by their teens they can speak multiple languages so fluently that they literally slip and weave between languages mid-speech.
Apparently their ability word-smith (say EXACTLY what they mean) is much much higher.

Yes and no. I'm fully bilingual, and all too often I find myself knowing the exact word for what I mean - in the language my audience does not speak. Finding the equivalent in the other language is very hard because I'm too aware of the fine nuances of meaning. So while I have a very big vocabulary to draw on when I'm trying to crystallize my thoughts, I'm at something of a disadvantage when I have to speak or write them. The "partial" vocabulary I'm forced to use feels crippling.