8 spheres and 1 weighing scale. 1 sphere weighs differently from other 7. What is the minimum number of steps needed to identify the different sphere.

Question

Accepted Answer

First Weighing: Divide the 8 spheres into three groups: two groups of 3 spheres each and one group of 2 spheres. Weigh the two groups of 3 spheres against each other.

If the scales balance, the odd-weighted sphere is among the remaining 2 spheres.
If the scales do not balance, the odd-weighted sphere is among the 3 spheres on the heavier or lighter side.
Second Weighing:

If the scales balanced in the first weighing, weigh the remaining 2 spheres against each other. The heavier or lighter one is the odd sphere.
If the scales did not balance in the first weighing, take the group of 3 spheres from the heavier or lighter side. Weigh 2 of these 3 spheres against each other.
If the scales balance, the third sphere (not weighed) is the odd one.
If the scales do not balance, the heavier or lighter one is the odd sphere.

Thus, you can identify the different sphere in a minimum of 2 weighings

8 spheres and 1 weighing scale. 1 sphere weighs differently from other 7. What is the minimum number of steps needed to identify the different sphere.

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