Math 3012F: Applied Combinatorics Fall 2006 Midterm 1 ...

(a) What is the fewest number of balls she can select to be sure of having at least three balls of the same color? 2 + 2 + 2 + 1 = 7 The colors are the holes and the balls are the pigeons. We need to force there to be 3 pigeons in at least one of the holes. If we select six or fewer balls, then there could be at most 2 pigeons in every hole. ................
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