The lighter coin

Logic Level 1

You have nine coins and you know that one of them is lighter than the other eight which have the same weight. Is it possible to determine the lighter coin by weighing twice with a two-pan balace?

Yes No

Luiz Claudio by Luiz Claudio , 19, Brazil

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2 solutions

Chew-Seong Cheong
Apr 21, 2019

Follow the steps below:

  1. Separate the nine coins into three groups of three coins.
  2. Weigh two groups of three coins with one group in a pan. If it is balanced then the group not weighed has the lighter coin. If it is unbalanced then the lighter group has the lighter coin. This means that with the first weighing we can find the group that has the lighter coin.
  3. Weigh two coins from the lighter group with one coin in a pan. If it is balanced then the coin not weighed is the lighter coin. If it is unbalanced then the lighter one is the lighter coin.

Yes , with two weighing on a balance, we can determine the lighter coin out of the nine coins..

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Joshua Lowrance
Apr 20, 2019

First weighing: separate the nine coins into three groups of three. Weigh one of the groups against another one of the groups (leaving one group of three on the side). We are attempting to find the group of three that contains the lighter coin. If on the scale, it shows that one group of three is lighter than the other, choose the group that is lighter. If both groups of three of are equal weight, then the one group of three that is on the side contains the lighter coin.

Second weighing: take the group of three that has the lighter coin. Weigh one of the coins against another of the coins (leaving one coin to the side). If one of the coins on the scale is lighter, the scale will show it, and there is your lighter coin. If the scale shows that the two coins are equal, the lighter coin is the one to the side.

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