## Friday, August 25, 2006

### Logical thinking in mathematical problem solving

This example requires some logical thinking:

4 boys

4 boys A,B,C,D sit in a straight line, facing 1 direction. They cannot turn their heads or leave their chairs. A wall seperates A and B. They are told that 2 black and 2 white hats are placed on their heads.

A and C are wearing black hats, while B and D are wearing white hats.

D can see B and C's hats, C can see B's hat. B is facing the wall, and A cannot see any hat, since he is on the other side of the wall.
They are only given 1 chance to get their own hats right by shouting out the answer. After 1 minute, someone calls out?

1) Who called out? How can he be 100% sure?
2) Explain how each boy managed to figure out their hat's color.

( Problem courtesy of Cassandra)

the logic goes in this sequence

1)the 3rd from left will keep quiet as obviously he do not know

2)the 2nd from left will keep quiet as he do not know too

3)the 1st from left will keep quiet as he do not know too

4) 2nd seeing 1st keeping quiet knew that he himself and the 3rd will not be the same colour so he shouted out black (different from 3rd)

5) 3rd by this time also know that he must be of different colour to 2nd, so he shouted white ...