You are given 12 balls, one of which is either heavier or lighter. Using a balance scale 3 times, find the odd ball and determine if heavy or light.

You are given 12 balls, one of which is either heavier or lighter. Using a balance scale 3 times, find the odd ball and determine if heavy or light.

Approach: Use information theory: 3 weighings give 3³=27 outcomes, need to identify 24 possibilities (12 balls × 2 states).

First weighing: 1,2,3,4 vs 5,6,7,8. If equal, odd in 9-12. Second: 1,2,3 vs 9,10,11. Third depends on outcomes. Systematic solution uses coding scheme.

Follow-up: What about 13 balls?

Key concepts: information theory, ternary coding, weighing strategy.