The Pot of Beans - Can you solve it?

7. The Pot of Beans

A pot contains 75 white beans and 150 black ones. Next to the pot is a large pile of black beans.

A somewhat demented cook removes the beans from the pot, one at a time, according to the following strange rule: He removes two beans from the pot at random. If at least one of the beans is black, he places it on the bean-pile and drops the other bean, no matter what color, back in the pot. If both beans are white, on the other hand, he discards both of them and removes one black bean from the pile and drops it in the pot.

At each turn of this procedure, the pot has one less bean in it. Eventually, just one bean is left in the pot. What color is it?

Added 1 January 2007

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Solution:

White. The cook only ever removes the white beans two at a time, and there are an odd number of them. When the cook gets to the last white bean, and picks it up along with a black bean, the white one always goes back into the pot.

Comments (4)

Anonymous 13 September 2008

The Pot of Beans puzzle is wrong.

Anonymous 21 September 2010

In the Pot of Beans puzzle, the final bean left in the pot will always be white due to the rules of bean removal.

Anonymous 3 June 2011

The Pot of Beans puzzle seems to contain an error that needs clarification.

Anonymous 16 April 2012

The cook's action of removing two white beans doesn't make sense. If he did, there would still be 150 black beans left, meaning the remaining bean would be a white bean among the black ones.

Logic Puzzles

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