1) Three bright children are in a Mensa classroom. The teacher says, "You’re all obedient and very intelligent. Here’s a little IQ test that is fair to each of you. Close your eyes. I’m going to place a red or blue hat on each of your heads. When I say ‘open’, you will open your eyes. If either of the other children is wearing a red hat, clap your hands once. When you know the colour of the hat on your own head, clap twice more. The children, being Mensa members, understood the instructions clearly. They closed their eyes, and the teacher put red hats on each of their heads. The teacher said ‘open’. The children opened their eyes. They all clapped once immediately. After a few moments, the third child clapped twice more and said his hat was red. How did the child know?
2) The same classroom situation as before. This time, after the children opened their eyes, the third child clapped three times right away and said all the hats were red. How did the child know??
The answers to September’s puzzles were supplied in the September issue.
Here are the answers to this month’s puzzles:
1). The third child reasoned that since all three clapped, there had to be at least two red hats. If the third child had a blue hat, child #1 or #2, being very intelligent, would know the other two hats were red and his/hers was therefore red. But neither of them clapped. Therefore, #3’s hat was red.
2) While the teacher talked, the third child reasoned: the test is fair. But if the teacher gives us hats that aren’t the same colour, the test won’t be fair. So all the hats will be either red or blue. As soon as the child saw that the other hats were red, the child knew his/hers was red too.
