December 09, 2018

Horse 2494 - The Highest Impossible Number of Chicken McNuggets

This afternoon after playing indoor football, some of use retired across the street to McDonald's for some Frozen Coke. Behind the counter there was a frantic panic as they'd run out of frozen slushee mixture on account of one person buying enough to drown a horse, and their second cause of panic was that they'd run out of Chicken McNuggets.
Me being the kind of person who questions these things, wanted to know the highest number that you couldn't buy. For that I needed some basic information.

Chicken McNuggets are sold in packs of 3, 6, 10 and 20. That means that once you arrive at the first number which ends in a particular digit, that all integers of Chicken McNuggets to infinity and beyond can be sold on account of the fact that there are packs of 10. Packs of 20 are already irrelevant to thinks because 20 could already be made up of 2 packs of 10.

1 - you can't buy 1 nugget
2 - you can't buy 2 nuggets
3 - is a packet; so all numbers ending in 3 are out.
4 - you can't buy 4 nuggets
5 - you can't buy 5 nuggets
6 - is a packet; so all numbers ending in 6 are out.
7 - you can't buy 7 nuggets
8 - you can't buy 8 nuggets
9 - can be made of 3 packets of 3; so all numbers ending in 9 are out.
10 - is a packet; so all numbers ending in 0 are out.
11 - you can't buy 11 nuggets
12 - can be made of 4 packets of 3; so all numbers ending in 2 beyond 12 are out.
14 - you can't buy 14 nuggets
15 - can be made of 5 packets of 3; so all numbers ending in 5 beyond 15 are out.
16 - can be made from a packet of 6 and a packet of 10; so all numbers ending in 6 beyond 16 are out.
17 - you can't buy 17 nuggets
18 - can be made of 6 packets of 3; so all numbers ending in 8 beyond 18 are out.
21 - can be made of 7 packets of 3; so all numbers ending in 1 beyond 21 are out.
27 - can be made of 9 packets of 3; so all numbers ending in 7 beyond 27 are out.

That means that the most number of Chicken McNuggets that you can not buy are 17.

Of course I have no idea why you'd even want to buy any Chicken McNuggets at all; considering that they're just Ingham nuggets which are already found in the supermarket and you could just as easily buy one big schnitzel from the deli counter anyway.

Now you know.

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