12-Ball Balance Puzzle

One of 12 balls has a different weight, but you do not know whether it is heavier or lighter. The challenge is to identify the ball and the direction of the difference in only three balance-scale weighings.

Possible states
12 × 2 = 24
Any one ball may be heavy or light.
Information available
3³ = 27
Each weighing has left-heavy, balanced, or right-heavy outcomes.
Goal
24 → 8 → ≤3 → 1
Each weighing narrows the candidate set.
Difference

The three fixed weighings

← left heavier   = balanced   → right heavier

Candidate states

24 remaining
Why this construction works

Each ball has a three-weighing placement signature: left pan, right pan, or off the scale. The signatures are chosen so that no two heavy/light possibilities generate the same three outcomes.

If the odd ball is heavy, its placement pushes the scale one way; if it is light, every non-balanced direction reverses. That lets the same three tests determine both which ball is odd and whether it is heavier or lighter.

Reference: Wikipedia — Balance puzzle, 12-ball problem