That Lunch Lady

Number Theory Level 4

A lunch lady at a certain school only sells chicken nuggets that are all identical. They nuggets come in boxes of 6, 9, and 20. You cannot buy a fraction of a meal or a different amount of chicken nuggets. If all the chicken is free, and you can buy as many boxes as you want, what is the greatest amount of chicken nuggets you cannot obtain?


The answer is 43.

Andrew The by Andrew The , 20, USA

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2 solutions

Checking all the numbers, we see that the numers 44, 45, 46, 47, 48 and 49 are the first six numbers in a row that can be obtained. Above that, every number can be expressed as n+6, being n a number which can be obtained, as all numbers from 44 to 49 can, and so can 50 to 55, an then can 56 to 61 etc. Taking that in account, we only have to check nubers from 0 to 43. The largest number in that list that can't be obtain is 43, and so it is the answer to this problem.

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Alex Jin
Apr 26, 2015

Through using just sixes and nines you can obtain all multiples of three larger than three. Through using a 20 and sixes and nines you can obtain all numbers one less than a multiple of three that are greater than 23. Through using two 20s and sixes and nines you can obtain all numbers greater than 43 that are one more than a multiple of three, so therefore the greatest number that cannot be obtained is 43.

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