By: Ian Larson

Did you know that 43 is the largest natural number that is not an original McNugget number?

McNugget numbers are based on the idea of Frobenius numbers AKA coin problems which were made by Ferdinand Georg Frobenius. These coin problems were to see what the maximum number of values that you can’t make with 2 values is, as if they are the values of coins. For example, if you had a coin worth 3 and a coin worth 5, you could make any number above 7.

McNugget numbers were introduced by Henri Picciotto in ‘Games Magazine’ in 1987. A McNugget number is any number of McNuggets you can order, and originally the McNuggets came in boxes of 6, 9, and 20. This meant that the largest number of McNuggets that you were
not able to get was 43 McNuggets. You can prove this by the fact that you are able to get 44, 45, 46, 47, 48, and 49 McNuggets, and if you add boxes of 6 to any of these you are able to get any number greater than 43.

In modern day, you are actually able to get 43 McNuggets. In most locations in Europe and Asia, a box of 4 McNuggets was added to the menu. This made it so you were able to order 43 McNuggets. I was personally able to order 43 McNuggets, as is shown in the image for this article. With this 4 piece box, you are actually able to order any amount of McNuggets that is greater than 11. In fact if you are able to get McNuggets from one of these locations and Japan, which has their McNuggets in boxes of 5 and 15, you are able to order any amount greater than 7. It is likely that nobody has ever ordered 11 McNuggets because you have to order McNuggets from multiple countries.

McNugget numbers are a very interesting and weird math concept. I hope McNugget numbers were as interesting to you as they were to me.