# Sorting out how many

Seven Brownies and three Leaders have baked 35 chocolate cupcakes and eaten them all. One Leader ate one cupcake, another Leader ate two cupcakes, and the third Leader ate three cupcakes. Only whole cupcakes may be eaten. Show that at least one (greedy)Brownie ate at least 5 cupcakes.

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its ok i know.... –  amy Feb 24 '13 at 15:09
6 cupcakes between 7 leaders then only 29 cupcakes left.. then if you give 5 cupcakes to a brownie (the greedy 1) there will be 24 left.this means the 6 brownies without the cupcakes can have 4 each. –  amy Feb 24 '13 at 15:10
As the leaders eat 6 cupcakes in total, there are 29 left. There are 7 brownies, if each of them ate at most 4 cupcakes, they'd eat $7 \cdot 4 = 28$ cupcakes in all, not the 29. So at least one must have eaten more than 4.