Answer 1
To find the correct switch (1, 2, or 3), turn switch 1 to ‘on’ and leave it like that for a few minutes. After that you turn switch 1 back to ‘off’, and turn switch 2 to ‘on’. Now enter the room. If the light bulb is lit, then you know that switch 2 is connected to it.
If the bulb is not lit, then it has to be switch 1 or 3. Now touching for short the light bulb, will give you the answer: if the bulb is still hot, then switch 1 was the correct one; if the bulb is cold, then it has to be switch 3.
Answer 2
Man A is wearing a white hat.
An explanation:
From the fact that neither B nor C gives an answer, we conclude that both these men have insufficient information to determine the color of their hats. Let us start with man C. He must be seeing at least one white hat on the heads of A and B (if he would see two black hats, he would know that he is wearing a white hat). Man B therefore knows that he and/or A is wearing a white hat.
Since he cannot give an answer, he must be seeing a white hat on A’s head (if B would see A wearing a black hat, he would know that he himself wears a white one). From the fact that neither C nor B can give an answer to the jailer’s question, A finally concludes that he is wearing a white hat!
Answer 3
There are several ways to solve this problem. An elegant solution is shown below.
Number the coins from 1 up to 12. Perform the following three weighings:
Left side: Right side:
Weighing 1: 1 2 3 10 4 5 6 11
Weighing 2: 1 2 3 11 7 8 9 10
Weighing 3: 1 4 7 10 3 6 9 12
Call the outcome of a weighing “L” if the left side is most heavy, call the outcome “R” if the right side is most heavy, and call the outcome “B” if the left and right sides have the same weight. Then the following outcomes are possible:
W1: W2: W3: Different coin:
L L L 1 heavier
L L R 3 heavier
L L B 2 heavier
L R L 10 heavier
L R B 11 lighter
L B L 6 lighter
L B R 4 lighter
L B B 5 lighter
R L R 10 lighter
R L B 11 heavier
R R L 3 lighter
R R R 1 lighter
R R B 2 lighter
R B L 4 heavier
R B R 6 heavier
R B B 5 heavier
B L L 9 lighter
B L R 7 lighter
B L B 8 lighter
B R L 7 heavier
B R R 9 heavier
B R B 8 heavier
B B L 12 lighter
B B R 12 heavier
Note: outcomes LRR, RLL, and BBB are not possible.
