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Number Theory

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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