Hint 1 for the 12 billiard balls maths prize

Often in maths it is good to start with a simplified version of the problem, or to start at the end and work backwards.

And it’s often good first to think about the *shape* of the answer before plunging into trying to work out details.

Those bits of advice all point the same way here. Think first about the *third* (last) weighing.

You’ve started with 12×2=24 possibilities: the odd ball may be any one of 1 to 12, and it may be heavy or light.

Your two first weighings must have narrowed the range. *To how few possibilities?*

Click here for hint 2

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