### Brain Teasers

# Buying a Puppy

A man wishes to sell a puppy for $11. A customer wants to buy it but only has foreign currency. The exchange rate for the foreign currency is 11 round coins = $15, 11 square coins = $16, 11 triangular coins = $17. How many of each coinage should the customer pay?

### Answer

7 circular coins and 1 square coin.Let x be the number of circular coins, y be the number of square coins, and z be the number of triangular coins. Thus:

x*(15/11) + y*(16/11) + z*(17/11) = 11.

Multiplying by 11:

15x + 16y + 17z = 121.

From here we have to use trial and error or educated guessing. Personally I divided 121 by 15 to get 8 plus a remainder of 1. It was then obvious that x=7, y=1, and z=0 would solve the equation.

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## Comments

I'm still stuck on this one...It's great.

there may be more than one answer, given the numbr of unknowns. a computer could number crunch and spit out all answers.

A pocket full of triangular coins...be careful how you sit down!

Great teaser. This is a unique solution.

I did it pretty much the same as the answer minus the algebra. Figures I needed 121/11 and then divided by 15 and got the answer.

This is the only solution, and I don't need a computer or exhaustive analysis to prove it.

It's easy to see that there can't be any other solutions with eight coins as the solution has only one coin more than the minimum possible with eight. So if there are any other solutions they must have no more than seven coins. 7 x 17 = 119, so there are no solutions with less than eight coins.

This is the only solution, and I don't need a computer or exhaustive analysis to prove it.

It's easy to see that there can't be any other solutions with eight coins as the solution has only one coin more than the minimum possible with eight. So if there are any other solutions they must have no more than seven coins. 7 x 17 = 119, so there are no solutions with less than eight coins.

"...as the solution has only one DOLLAR more than the minimum."

I did it the same way as Java minus the proof of uniqueness. Good teaser even better explanation. (One of the things I like about this site is that many of the inciteful comments generated are often more exciting and educational than the teasers themselves.)

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