Monday, March 24, 2008

Easter Egg Hunt

You are invited to an Easter egg hunt party having 100 colored Easter eggs hidden in the backyard. 20 eggs are colored red, 14 eggs are colored blue, 15 eggs are colored green, 16 eggs are colored brown, 17 eggs are colored yellow and 18 eggs are colored orange. All of these eggs are wrapped with golden wrappers. What is the minimum number of eggs that you should find so that you are sure that you have at least 2 pairs of similarly colored eggs. For example, 2 red eggs and 2 blue eggs. You can also have 2 yellow eggs together with another set of 2 yellow eggs.

1. I believe the answer is nine.

The maximum # of eggs for which you won't have a pair is six. If you add one more, you will definitely have one pair. Add one more and, if it's the same color as the seventh egg, you won't have a second pair. Add in the ninth egg, and you're guaranteed to have at least two pairs.

2. 9

worst case, you pick 6 different eggs on your first 6. then, on the 7th, you are bound to get a pair. your 8th might be a third of the same egg, so you have to get 9.

3. oops...you beat me by 2 minutes, apparently...

4. I win, I win!

Oh... wait...

:-)

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