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Date: 03/10/2002 at 23:47:36
From: Roxanne
Subject: McNuggets

Dear Doctor Math,

I kind of think that this is a trick question, but I'm not sure. 
Can you help me with it? 

At one McDonald's location, McNuggets come in boxes of 6, 9, and 20. 
What would be the largest number of McNuggets that you could not buy?

Thank you for your time,

Date: 03/11/2002 at 22:49:10
From: Doctor Twe
Subject: Re: McNuggets

Hi Roxanne - thanks for writing to Dr. Math.

No, it's not a trick question. After a while, you get to a point where 
if you have some number X of McNuggets, you can get X+1 McNuggets 
by "trading" either:

   -> a 20-box for a 9-box and two 6-boxes  (-20 + 9 + 2*6 = +1)


   -> three 9-boxes for a  20-box and a 6-box (-3*9 + 20 + 6 = +1)

But I have to have enough McNugget boxes to make those trades, so at 
some low numbers - like 16 (from 6+9 = 15) or 19 (from 2*9=18) - I 
can't make those trades. There is a largest number *not* makeable.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum   
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