Question

a shop sells sweets in bags of 7 and 20 what is the largest number of sweets that cannot be purchased exactly?

Answer 1

By the Frobenius Coin Theorem, also known as the Postage Stamp Theorem or the Chicken McNugget Theorem, the maximum amount that cannot be represented as a sum of multiples of two relatively prime numbers a and b (numbers that have GCF of 1) is ab-a-b.  Plugging 7 and 20 in, our answer is 7*20-7-20, or 140-27, or 113.