You are given 12 balls, 11 are identical, one is heavier. How do you find the heavier ball in only 3 moves?

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Here's the problem. You are given 12 balls and a scale. Of the 12 balls, 11 are identical and one way slightly more. How do you find the heavier ball amongst these 12 using the scale only 3 times.

Here's the solution.

Take 5 balls and 5 balls and weigh them. If the scales are equal, you can discard the 10 balls and just weigh the other 2 to get your answer. That would be the 2nd use of the scale, in which case you have found the heavier ball into moves.

If on the other hand, the 1st weighing of 5 and 5 balls, one group is heavier, then, of the heavier group, way too against 2 (that's the 2nd use of the scale) and if they weigh the same, the 5th ball is the one that you are looking for.

If 1 of the groups of 2 balls is heavier, then take the heavier group of 2 balls and weigh them against each other (that's the 3rd use of the scale) and you'll find the heavier ball is the one that you are looking for.

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0 Response
  1. boerenbrommer

    My solution was different: weigh 6 on both sides, continue with heavier group of 6 and put 3 on both sides. Take heavier group of 3 and put any 2 of the remaining balls on the scale (1 on each side). If their equal, the ball you didnt use is the heaviest. If its not equal, youll simply see which is the heavier one.
    By the way, your brain teaser videos are my favorite thing on youtube so please keep making them! Thanks 🙂

  2. boerenbrommer

    My solution was different: weigh 6 on both sides, continue with heavier group of 6 and put 3 on both sides. Take heavier group of 3 and put any 2 of the remaining balls on the scale (1 on each side). If their equal, the ball you didnt use is the heaviest. If its not equal, youll simply see which is the heavier one.
    By the way, your brain teaser videos are my favorite thing on youtube so please keep making them! Thanks 🙂

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