# Thread: Coin Conundrum / Puzzle

1. ## Coin Conundrum / Puzzle

Here is a puzzle that I have been having difficulty with. Let me know what you think.

Your friend and you are in a standard American mall and see a vending machine. Your friend pulls out a crisp \$1 bill to buy a 95 cent candy bar, but then realizes that the machine takes exact change only. Your friend turns to you and asks if you could break a dollar. You reach into your pocket and fish out 6 coins, which add up to \$1.15 saying, "Well, with this amount I should be able to break a bill ... but it appears that I cannot!" Upon further examination, you see that you cannot give change for a 50 cent piece, a quarter, a dime, or even a nickel with the 6 coins you have.

Frusturated, your friend asks you to just buy him the candy bar and you realize... you cannot buy the 95 cent candy bar.

What are the 6 coins that you have?

My attempt is in the spoiler. Only read the spoiler if you attempted the puzzle by yourself to garuntee a fresh mind!
Spoiler

2. 2 \$.25
1 \$.50
3 \$.05

3. Except with those coins you CAN give change for a 50 cent coin, for a one dollar bill, and for a dime.

4. I'm not sure this is even possible.
You can't have more than 1 \$.50, because then you'd be able to break \$1.
You can't have more than 1 \$.25, because then you'd be able to break \$.50.
With 1 \$.50 and 1 \$.25, you need \$.40 more in four coins. The only way this is possible is with 4 \$.10. This, however, allows you to add up to \$.95.
Without one of the \$.50 or \$.25 (or both of them), it's impossible to add up to \$1.15 in only six coins.
Am I interpreting the question incorrectly?..

5. Gonna put my thinking in spoiler too.
Spoiler

6. There's no solution unless there's a coin denomination other than \$1, \$0.25, \$0.10, \$0.05 and \$0.01.

Here's proof.

• Observation 1: \$1 coin is not one of the 6 coins. Because adding up to exactly \$0.15 from 5 coins is impossible.
• Observation 2: You can have at most 1 \$0.50 coin. Because if you had more than 1 \$0.50 coin then you could change for \$1 bill.
• Observation 3: You can have at most 1 \$0.25 coin. Because if you had more than 1 \$0.25 coin then you could change for \$0.5.
• Theory A: One of the 6 coins is a \$0.50 coin.
Implication: The other 5 coins add up to exactly \$0.65.
• Theory a: One of the 5 coins is a \$0.25 coin.
Implication: The other 4 coins add up to exactly \$0.40.

Then the 4 remaining coins must be all \$0.10 coins. Because if they were a lesser demonination they would add up to less than \$0.40.

However this combination can produce exact change for \$0.95 with 1 \$0.50, 1 \$0.25 and 2 \$0.10 and therefore is wrong.

Conclusion a: None of the 5 coins is a \$0.25 coin.

Implication: The highest possible denomination for the 5 coins is \$0.10. However 5 * \$0.10 < \$0.65.
Conclusion A: None of the 6 coins is a \$0.50 coin.

• Theory B: One of the 6 coins is a \$0.25 coin.
Implication: The other 5 coins add up to exactly \$0.90. Since there cannot be more than 1 \$0.25, the highest possible denomination of these 5 coins is \$0.10.

However 5 * \$0.10 < \$0.90.

Conclusion B: None of the 6 coins is a \$0.25 coin.

Therefore the highest possible denomination for the 6 coins is \$0.10.

However 6 * \$0.10 < \$1.15.

Edit: damnit ninja

7. The unbalanced solution

9. I completely missed that part of the statement, heh.

10. Spoiler

11. Or they realize they're Canadians and all the coins they have are Canadian. In an American mall.
The currency type possessed is never mentioned. And looking at user flags...

Anyway, the six coins are a 50 cent piece, a quarter, and 4 dimes.

95 cents is just the goal. The challenge is to exchange the \$1 bill for coins (Can't do it).

12. you realize the confederacy lives on in the south when you pull out a \$1 coin and 5 3 cent pieces

...this problem don't wurk in amurrrka

13. Figured out the actual reason you can't buy it.
American vending machines don't accept coins larger than quarters.
Considering how uncommon 50 cent pieces are anymore, it makes sense.

14. Hey... F'uck you.

They're all using invalid coins, or coins of a different version i.e: 2 cent coins, etc.

15. i'm from tx/la

pineapple you too

16. Standard american mall. That probably means that there are no 3 cent coins.

17. what does the mall have to do with what's in your pocket?

18.

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