You’re on an island with 12 islanders. All of them have perfect logic skills and always tell the truth.
They’re also armed with spears, and look very angry. However, they have a task…
Among the islanders, 11 islanders weigh exactly the same, and one islander is slightly heavier or lighter.
A seesaw can be used to compare the weights of any two groups of islanders but can only be used three times.
How can you determine which islander has a different weight and whether they are heavier or lighter than the others by using the seesaw only three times?
If you fail, you can assume that your fate is sealed.
First, divide the 12 islanders into three groups: Group A with 4 islanders, Group B with 4 islanders, and Group C with 4 islanders.
- Use the seesaw to compare Group A and Group B: If the seesaw balances, the islander with a different weight is in Group C.
- If the seesaw does not balance, the islander with a different weight is in either Group A or Group B. Remember which group is heavier for the next steps.
For the second use of the seesaw, take three islanders from the group with the different-weight islander (either Group A, B, or C from step 2).
Compare one islander against another from the same group.
If the seesaw balances this time, it means the different-weight islander is the one not on the seesaw from the group in question, and they are either heavier or lighter based on the result from step 2.
If the seesaw does not balance, remember which side is heavier.
For the third use of the seesaw, take the two remaining islanders from the second comparison (step 3).
Compare one islander against any of the islanders you know to be of equal weight (one from either Group A or B if the different-weight islander was in Group C, or one from Group C if the different-weight islander was in Group A or B).
If the seesaw balances this time, it means the different-weight islander is the one not on the seesaw from the pair in step 5, and they are either heavier or lighter based on the result from step 4.
If the seesaw does not balance, it means the islander on the seesaw from the pair in step 5 is the different-weight islander, and they are heavier or lighter based on which side of the seesaw is higher.
By using the seesaw three times, you can identify the islander with a different weight and whether they are heavier or lighter than the others.
