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Finding a lighter or heavier ball out of 12 balls, with only three weighings allowed

You have 12 balls out of which one is odd ie lighter or heavier than others. You can't identify the odd ball just by looking at it. So, how you would find out the ball, using the weighing scale and maximum weighings allowed are three only?

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Let's first divide 12 balls into there groups of 4 each. First take two groups of four each and weigh on the scale.

Case -1
Both the groups are equals
Odd ball is in third group of four balls.

Now Let's take three balls from the first two groups and three balls from the last group.

Either equals or nor equal.

Case 1.1:
Both the groups of three are equal
i.e. The fourth ball in the third group is odd.

Now weighing this ball against any other ball will tell, us whether the odd ball is lighter or heavier than others.

Case 1.2
Both the ...

Solution Summary

A lighter or heavier ball out of 12 ballsis found, with only three weighings allowed. The solution is detailed and well presented.