There are 12 men on an island. 11 weigh the same. 1 man is heavier or lighter. There is one seasaw you can use only 3 times. How do you find the odd man out?
1. First weigh men 1,2,3,4 vs 5,6,7,8.
If they are equal:
2. weigh men 9,10,11 vs 1,2,3.
If they are equal than man 12 is the different one and use the third weigh to determine if he is heavier or lighter(ie. 3. man 12 vs 1).
If they are unequal 3. weigh man 9 vs 10. You already know if the different man is heavier or lighter from the second weigh so whichever one is heavier or lighter as per the second weigh is the answer. If they are balanced man 11 is heavier or lighter.
If they aren't equal:
I'm going to assume the 1,2,3,4 men were lighter (It doesn't matter which side was lighter as you can always flip them). This tells us that either 1,2,3,4 is light or 5,6,7,8 is heavy. Then 2. weigh men 1,2,3,5 vs 4,9,10,11. L
If the 1,2,3,5 side is lighter, that means either 1,2 or 3 is lighter. 3. Weigh man 1 vs 2. Whichever is lighter is the answer.
If they are equal, it is man 3.
If the two sides were balanced, that means either 6, 7, or 8 is heavier. Then 3. Weigh man 6 vs 7. Again, whichever is heavier is the answer. If they are equal, it is man 8.
Finally, if the 4,9,10,11 side was lighter, that tells us that either 5 is heavier or 4 is lighter. 3. Weigh man 4 vs 1. If 4 is lighter, that is the answer. Else, 5 is the heavier man.
1. First weigh men 1,2,3,4 vs 5,6,7,8.
If they are equal:
2. weigh men 9,10,11 vs 1,2,3.
If they are equal than man 12 is the different one and use the third weigh to determine if he is heavier or lighter(ie. 3. man 12 vs 1).
If they are unequal 3. weigh man 9 vs 10. You already know if the different man is heavier or lighter from the second weigh so whichever one is heavier or lighter as per the second weigh is the answer. If they are balanced man 11 is heavier or lighter.
If they aren't equal:
I'm going to assume the 1,2,3,4 men were lighter (It doesn't matter which side was lighter as you can always flip them). This tells us that either 1,2,3,4 is light or 5,6,7,8 is heavy. Then 2. weigh men 1,2,3,5 vs 4,9,10,11. L
If the 1,2,3,5 side is lighter, that means either 1,2 or 3 is lighter. 3. Weigh man 1 vs 2. Whichever is lighter is the answer.
If they are equal, it is man 3.
If the two sides were balanced, that means either 6, 7, or 8 is heavier. Then 3. Weigh man 6 vs 7. Again, whichever is heavier is the answer. If they are equal, it is man 8.
Finally, if the 4,9,10,11 side was lighter, that tells us that either 5 is heavier or 4 is lighter. 3. Weigh man 4 vs 1. If 4 is lighter, that is the answer. Else, 5 is the heavier man.