# First Day Math Puzzle

August 29, 2007

Here’s a math puzzle that my son’s geometry teacher had them work on today, his first day of high school:

There are 75 white beans and 150 black beans in a jar, and another large pile of black beans outside of the jar. A person reaches into the jar and chooses 2 beans at random.

- If they are both black, keep one out, and put one back in
- If there is one of each color, keep the black one out and put the white one back in
- If they are both white, keep them both out

What will the color of the last bean left in the jar be?

(No, it has nothing to do with geometry. I guess it was just problem solving practice, and practice with using a certain format to write up problem solutions. I had seen the problem before, but had forgotten about it.)

3 Comments
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I believe the last bean will be white. There is no way to remove the last white bean, since you need two white beans to remove both of them. As there are an odd number of white beans, there will be one remaining at the end.

What is the purpose of the large pile of black beans outside the jar?

Oops, I forgot a detail of the puzzle. In one of the situations (probably when you took the 2 whites out), you were supposed to put an extra black back into the jar. So there needed to be enough outside of the jar to be sure you could do that when it came up. But the answer is still as you explained.

Ah, that makes sense! I was wondering because I couldn’t even see how it could function as a “red herring” since it seemed to have no connection whatsoever to the jar and associated beans!