On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 8 confusions and the other worth 11 confusions. There are also some coins of smaller value, but each weighs over 10 kilograms, so they are difficult to carry around.
Both questions go to that above! ^
1. In how many ways can a resident of Enigma use only bills to purchase a gyroscope that costs 97 confusions?
2. In how many ways can a resident of Enigma use only bills to purchase a single math book page that costs 69 confusions? (A page is so expensive because the residents of Enigma clearly don't understand much math.)
1 - There is only one way of buying a gyroscope which costs 97 confusions as follows:
[8 confusions x 8] + [3 confusions x 11] =64 + 33 =97 confusions
2 - There is NO WAY of buying a math-book page for 69 confusions. In fact, 69 is the largest number that you CANNOT make with 11 and 8 confusions. These are the numbers that you Cannot make with 11 and 8 confusions:
(1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 34, 36, 37, 39, 42, 45, 47, 50, 53, 58, 61, 69) >Total of all numbers that you CANNOT make = 35
