http://math.ucsd.edu/~mathclub/games/brainteaser-archive/chicken_mc_numbers.html

McDonald's sells Chicken McNuggets in packs of 6, 9, 20. You could purchase, say, 21 nuggets through the purchase of two 6-packs and one 9-pack. You cannot, regardless of how clever, purchase exactly ten nuggets. We'll say ten is an impossible number. Not all numbers are possible, but after a certain point, every number can be achieved. Find the largest impossible number.

Now suppose McD's sells x-packs and y-packs of nuggets, where x and y are relatively prime (that means, the greatest common factor of x and y is 1).

Find, with proof, a formula for the largest impossible number regardless of the choice of x and y.

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