The 8-ball weighing puzzle: you have 8 identical-looking balls; one is slightly heavier. Using a balance scale, find the heavy one in the minimum number of weighings.

2 weighings.

Weighing 1: split into groups of 3, 3, and 2. Put 3 vs 3. • If they balance, the heavy ball is in the leftover 2 → weigh those 1 vs 1, the heavier side is it (weighing 2). • If one side of 3 is heavier, the heavy ball is among those 3 → take any 2 of them and weigh 1 vs 1: if one is heavier that's it; if they balance, it's the 3rd untested ball (weighing 2).

Key insight: a balance scale gives 3 outcomes (left, right, equal) per weighing, so 2 weighings distinguish up to 3² = 9 cases — enough for 8 balls. Splitting into thirds, not halves, exploits the 'equal' outcome.