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The Chicken Nugget Conundrum

The Puzzler


RAY: This puzzler was sent in by a fellow named Louis Gee. Here it is:

There's a famous fast-food restaurant you can go to, where you can order chicken nuggets. They come in boxes of various sizes. You can only buy them in a box of 6, a box of 9, or a box of 20. So if you're really hungry you can buy 20, if you're moderately hungry you can buy 9, and if there's more than one of you, maybe you buy 20 and you divide them up.

Using these order sizes, you can order, for example, 32 pieces of chicken if you wanted. You'd order a box of 20 and two boxes of 6.

Here's the question:

What is the largest number of chicken pieces that you cannot order? For example, if you wanted, say 37 of them, could you get 37? No. Is there a larger number of chicken nuggets that you cannot get? And if there is, what number is it?

Think you know? Drop Ray a note!

[ Car Talk Puzzler ]

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