McNugget Problem and Frobenius Numbers

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McDonald's® once sold Chicken McNuggets™ in packs of 6, 9, or 20. What is the highest number of McNuggets™ you cannot buy? The answer is 43 because no combination of 6, 9, and 20 will add to 43. Any higher number can be bought. For packs of 9 and 20, the highest unbuyable quantity is 151. This Demonstration lets you control two values, and then plots the maximal unattainable number for a range of third values. In mathematics, these unattainable values are known as Frobenius numbers.

Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


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