Question: Twelve men are on a desert island, all with identical weights except for one of them, who is slightly lighter or heavier than the others. The only other thing on the island is a seesaw. There are no scales or means to measure weight otherwise. Can you determine which man has the different weight? You only get to use the seesaw three times
Answer:Number the men 1,2,3…12. First weigh 1,2,3,4 against 5,6,7,8. One of two things will occur:
1) They are equivalent. Presently we realize that the diverse man is among {9,10,11,12}. Weigh 9,10,11 against 1,2,3. In the event that these are equivalent, the diverse man is 12. Gauge 12 against 1 to see if 12 is heaver or lighter. In the event that the 9,10,11 varies from 1,2,3, at that point gauge 9 against 10. On the off chance that they are the equivalent, the diverse man is 11, and he is heavier if 9,10,11 was heavier than 1,2,3 and he is lighter if 9,10,11 was lighter than 1,2,3. In the event that 9 and 10 are extraordinary, the distinctive man is the lighter of the 9,10 correlation if 9,10,11 was lighter than 1,2,3, (and he is lighter); the diverse man is the heavier of the 9,10 examination if 9,10,11 was heavier than 1,2,3 (and he is heavier).
2) They are unique. Without loss of sweeping statement guess that 1,2,3,4 is heavier than 5,6,7,8. (We could generally relabel the men so this is valid). We know {9,10,11,12} all gauge the equivalent.
Weigh 1,2,5,6,7 against 8,9,10,11,12:
an) If 1,2,5,6,7 is heavier, at that point either 1 or 2 heavier, or 8 is lighter. Gauge 1 against 2. In the event that they are extraordinary, the heavier of the two is the one we are searching for (and heavier). In the event that they are the equivalent, 8 is the one we are searching for (and lighter).
b) If 1,2,5,6,7 is lighter, at that point one of 5,6,7 is extraordinary and lighter. Gauge 5 against 6. On the off chance that they are unique, the lighter of the two is the one we are searching for (and lighter). In the event that they are the equivalent, 7 is extraordinary (and lighter).
c) If they are the equivalent, at that point one of 3,4 is unique. Gauge them against one another. The person who is heavier is the distinctive man (and heavier).