Marble madness
Here is a puzzle I found on Maths is Fun. It is similar to the Five hats problem.
Puzzle
Years ago, to puzzle his friends, a scientist gave one of four containers containing blue and/or yellow marbles to each of the friends; Tom, Dick, Harry, and Sally.
There were 3 marbles in each container, and the number of blue marbles was different in each one. There was a piece of paper in each container telling which color marbles were in that container, but the papers had been mixed up and were ALL in the wrong containers.
He then told all of his friends to take 2 marbles out of their container, read the label, and then tell him the color of the third marble.
So Tom took two blue marbles out of his container and looked at the label. He was able to tell the color of the third marble immediately.
Dick took 1 blue marble and 1 yellow marble from his container. After looking at his label he was able to tell the color of his remaining marble.
Harry took 2 yellow marbles from his container. He looked at the label in his container, but could not tell what color the remaining marble was.
Sally, without even looking at her marbles or her label, was able to tell the scientist what color her marbles were. Can you tell what color marbles Sally had? Can you also tell what color marbles the others had, and what label was in each of their containers?
See Also
References
Maths is Fun - math and logic puzzles appropriate for math education.