What Is the Chicken McNugget Theorem?


Quick Answer

According to “McNugget Number,” the Chicken McNugget theorem generates positive integers that are obtained by adding together the numbers of Chicken McNuggets available in the original boxes containing 6, 9 and 20 McNuggets. Assuming that the boxes contain the correct number of McNuggets, the Chicken McNugget theorem tells you the largest number of McNuggets you cannot eat – 43.

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Full Answer

The Chicken McNugget theorem is a variation of the Coin Problem, which calculates the largest amount that a group of coins cannot add up to. For example, if you have one coin with a value of three and another with a value of five, the largest amount that they cannot equal is seven. McNugget numbers are Frobenius numbers, the largest number for which the Frobenius equation has no answer, given a specific data set. Therefore, using the original McNugget quantities of 6, 9 and 20, all positive integers are McNugget numbers except 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37 and 43. The Frobenius equation was developed by 19th-century German mathematician Ferdinand Frobenius, who worked in number and group theory. Henri Picciotto proposed the Chicken McNugget theorem in 1994 and published it an algebra textbook co-authored with Anita Wah.

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