Brain Teasers
The Egg Game
There are 2008 eggs lying in front of you. I am also with you waiting to start the game. The goal of the game is to be the person to take that very last egg (or eggs) to win. You and I can each only take between 1 and 100 eggs at a time. You go first. How many eggs must you take initially in order to always win (assuming we both play perfectly)?
Hint
By a perfect game, that means over any two turns, the sum of the number of eggs you and I take is the same (except of course, excluding the initial move you make).Answer
89 eggs.In order to see this, look at the smallest way possible to guarantee a win; you leave me with 101 eggs. If I take 1 egg, you take all 100; if I take 100 eggs, you take the last one. Therefore you would always win.
If you try with 202, I can take from 1 to 100, so there is 201 to 102 left. Then you would take 100 or 1 egg(s) in order to leave me with 101 again. By simple analysis, you must take 101 eggs over two rounds in order to get down to 101.
19*101 = 1919, so we must take 2008-1919 = 89 eggs to start off with a multiple of 101.
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Comments
My brain hurts.
It all fits.
GREAT TEASER!!!!!
This one is really fun and the first on my favorite teaser list.
This one is really fun and the first on my favorite teaser list.
I've played this game before! Except with 9 peanuts. Personally, I think this should be in math. But I'm not the smart one here.
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