## 12 balls (Solution)

Drew Reiner and I solved this together. I canâ€™t say that our method was particularly elegant, it was mostly just think about it for a long time and try lots of stuff. For a more complete dissection of this problem, I suggest looking here.

Number the 12 balls from 0 to 11.

Weigh: left = [0, 1, 2, 3] vs. right = [4, 5, 6, 7] If Left_heavy: Weigh: left = [0, 1, 2, 4] vs. right = [3, 8, 9, 10] If Left_heavy: Weigh: left = [0] vs. right = [1] If Left_heavy: Solved -> Ball 0 is heavy If Left_light: Solved -> Ball 1 is heavy If Even : Solved -> Ball 2 is heavy If Left_light: Weigh: left = [4] vs. right = [11] If Left_heavy: Impossible -> Impossible, all balls are equal If Left_light: Solved -> Ball 4 is light If Even : Solved -> Ball 3 is heavy If Even: Weigh: left = [5] vs. right = [6] If Left_heavy: Solved -> Ball 6 is light If Left_light: Solved -> Ball 5 is light If Even : Solved -> Ball 7 is light If Left_light: Weigh: left = [0, 1, 2, 4] vs. right = [3, 8, 9, 10] If Left_heavy: Weigh: left = [4] vs. right = [11] If Left_heavy: Solved -> Ball 4 is heavy If Left_light: Impossible -> Impossible, all balls are equal If Even : Solved -> Ball 3 is light If Left_light: Weigh: left = [0] vs. right = [1] If Left_heavy: Solved -> Ball 1 is light If Left_light: Solved -> Ball 0 is light If Even : Solved -> Ball 2 is light If Even: Weigh: left = [5] vs. right = [6] If Left_heavy: Solved -> Ball 5 is heavy If Left_light: Solved -> Ball 6 is heavy If Even : Solved -> Ball 7 is heavy If Even: Weigh: left = [0, 1, 2] vs. right = [8, 9, 10] If Left_heavy: Weigh: left = [8] vs. right = [9] If Left_heavy: Solved -> Ball 9 is light If Left_light: Solved -> Ball 8 is light If Even : Solved -> Ball 10 is light If Left_light: Weigh: left = [8] vs. right = [9] If Left_heavy: Solved -> Ball 8 is heavy If Left_light: Solved -> Ball 9 is heavy If Even : Solved -> Ball 10 is heavy If Even: Weigh: left = [11] vs. right = [0] If Left_heavy: Solved -> Ball 11 is heavy If Left_light: Solved -> Ball 11 is light If Even : Impossible -> Impossible, all balls are equal