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    • Weighing balls: Solution

      31 October, 2016
      Scales

      Note that you're allowed to put more than one ball in each pan.

      Suppose you are given eight balls and you know that one ball is slightly heavier than all the others, which are of equal weight. You're also given a balancing scale with which you can compare the weight of balls by putting some in one pan and some in the other. What's the minimum number of weighings you need to establish which ball is the heavier one?

      Solution

      The answer is two. Split the balls in two groups of three and one group of two. Compare the two groups of three using the scale. If one is heavier than the other, pick two balls from the heavier group and compare them on the scale. If one of them is heavier than the other, then that's your answer. If they weigh in equally, then the heavier ball is the one you didn't pick.

      If the two groups of three balls weigh in equally, then the heavier ball is among the group of two. You can compare these using one further weighing, which will give you your answer.

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      Shahram Najm

      13 November 2016

      Permalink
      Comment

      It's log base 3 of N ( number of balls )

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      Leslie.Green

      10 September 2018

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      Comment

      We solve this problem on the basis that the balance scales give three possible results: left heavy, right heavy, equal. They don't actually work that way. The pivot is typically so sensitive that any slight imbalance will cause a left or right down situation. In order to solve the problem we have to suspend disbelief and pretend that the scales will actually balance. Maybe the bearing is a little sticky, or maybe we note that it doesn't fall very quickly - which we then interpret as a balanced state.

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      Mr MJ

      24 May 2020

      In reply to Balance Scales are not tri-state devices by Leslie.Green

      Permalink
      Comment

      It's log 3 base N

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      Jonah

      6 April 2022

      In reply to Balance Scales are not tri-state devices by Leslie.Green

      Permalink
      Comment

      We don't have to suspend belief if (a) the balance scales ARE accurate and sensitive, and/or the heavier ball is heavier enough to make a significant difference in the balance

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