A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggetsTM (prior to consuming any), which originally
came in boxes of 6, 9, and 20 (Vardi 1991, pp. 19-20 and 233-234; Wah and Picciotto
1994, p. 186). All 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 value 43 therefore
corresponds to the Frobenius number of .
Since the Happy MealTM-sized nugget box (4 to a box) can now be purchased separately, the modern McNugget numbers are linear combinations
of 4, 6, 9, and 20. These new-fangled numbers are much less interesting than before,
with only 1, 2, 3, 5, 7, and 11 remaining as non-McNugget numbers. The value 11 therefore
corresponds to the Frobenius number of .
The greedy algorithm can be used to find a McNugget expansion of a given integer . This can also be done in the Wolfram
Language using FrobeniusSolve[
6, 9, 20
, n]. The following table summarizes (classic) McNugget
expansions for small integers.
McNugget expansions | |
6 | |
9 | |
12 | |
15 | |
18 | |
20 | |
21 | |
24 | |
26 | |
27 | |
29 | |
30 |