Pebble Problem

A merchant owed a large sum of money to a lender. The old, ugly moneylender fancied the merchant’s beautiful daughter. He proposed that he would forget the debt if he could marry the merchant’s daughter. The merchant and his daughter were horrified.

The moneylender suggested that they let providence decide the matter. He told them that he would put a black pebble and a white pebble into an empty bag. The girl would pick a pebble from the bag. If she picked the black pebble she would have to marry the moneylender and the debt would be forgotten. If she picked the white pebble, she need not marry him and the debt would be forgotten. If she refused to pick a pebble the merchant would have to go to jail.

The moneylender bent over and picked up two pebbles. The sharp-eyed girl noticed that he had picked up two black pebbles and put them into the bag. The girl immediately agreed to the contest despite her father’s protests.

Why did she agree?

On first impression it would seem there were only three possibilities:

  1. She refuses to take a pebble, sending her father to debtors prison.
  2. She shows that there were two black pebbles exposing the cheating moneylender but leaving the her father in debt.
  3. She picks a black pebble and sacrifices herself for her father’s freedom.

Before you read the answer, below, try to solve this problem yourself.

You need no other information.

There is a solution.

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The girl nervously picked a pebble out of the bag, fumbled, and dropped it on the ground so that it couldn’t be known what color it was. She then said: “Oh I’m so foolish, but never mind. We can look in the bag and see the color of the remaining pebble. We will then know what color my pebble was.”

Did you give up too soon? Look harder for the wise solutions to your own insoluble problems!