## Forty-three and Frobenius Numbers

This is a school project to summerize Numberphiles videos.

Forty-three is a very special number with chicken nuggets. It is the highest number that you can make using the standard packs of nuggets. The packs are nine, six, and twenty, the numbers that you can't make with the standrd packs of nuggets are: one, two, three, four, five, seven, eight, ten, eleven, thirteen, fourteen, sixteen, seventeen, nineteen, twenty-two, twenty-three, twenty-five, twenty-eight, thirty-one, thirty-four, thirty-seven, and forty-three. If you wanted to make forty-four, you would need a box of twenty, two boxes of nine, and a box of six. But now McDonalds has changed the rules, and they sell packs of four, six, nine, and twenty. Now all that you can't make is one, two, three, five, and eleven. So the highest number that you can't make with the standard packs of nuggets now is eleven. So how can you make forty-three? You can use three packs of nine, two packs of six, and a pack of four. These nugget numbers in the world of math, are called Frobenius numbers, and forty-three is the largest number you can't make with Frobenius numbers. Another name for this (the nugget problem) is the coin problem. So if you have coins of different values, what can you buy, and what can't you buy.