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.)

Rangcr897 Jul 9, 2024

#1**0 **

*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.

_{.}

Bosco Jul 10, 2024