16 Eggs and a Balance Scale

The problem
16 eggs · one is heavier · balance only

You have 16 eggs. They look identical, but exactly one is slightly heavier than the others. You have a balance scale — two pans, no calibrated weights, you can only compare which side is heavier.

What's the minimum number of weighings that guarantees finding the heavy egg?

Tempting (but wrong)
binary search · 8 vs 8 · log₂ 16 = 488throws away the "balanced" outcome

Binary search. Split 16 into two piles of 8 and weigh them. The heavier pan has the heavy egg. Repeat with 8 → 4 → 2 → 1.

That's 4 weighings, since log⁡216=4\log_2 16 = 4.

Clean reasoning. Wrong tool.