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On planet Enigma, the residents use a currency called the confusion.  There are only two confusion bills on Enigma, one worth $7$ confusions and the other worth $12$ confusions.  There are also some coins of smaller value, but each weighs over $10$ kilograms, so they are difficult to carry around.

In how many ways can a resident of Enigma use only bills to purchase a toaster that costs 19 confusions?

(Everybody knows, of course, that vendors on Enigma do not give change, so residents must make their purchases with exact change.)

 Jul 9, 2024
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On planet Enigma, the residents use a currency called the confusion.  There are only two confusion bills on Enigma, one worth $7$ confusions and the other worth $12$ confusions.  There are also some coins of smaller value, but each weighs over $10$ kilograms, so they are difficult to carry around.  In how many ways can a resident of Enigma use only bills to purchase a toaster that costs 19 confusions?   

 

I think nobody is answering this problem because it's so obvious that they suspect a trick.   

Well, I'll admit I'm suspicious, too, but I'll take one for the team.  I'm going out on that limb.  

 

There is only one way to purchase the toaster ... with one 7-confusion bill and one 12-confusion bill.   

.

 Jul 10, 2024

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