Balls with weighing scales maths game

Balls with weighing scales maths game

Question: 




You are given a set of weighing scales and 9 identical-looking balls. However, one of the balls is slightly heavier or lighter than the others, but you don’t know whether it’s heavier or lighter. Using the scales only twice, how can you identify the odd ball and determine whether it’s heavier or lighter than the others?














Answere:


1. Divide the 9 balls into 3 groups of 3 balls each.

2. Weigh two of the groups against each other:

• If the scales balance, the odd ball is in the third group.

• If one side is heavier, the odd ball is in that group.

3. Take the group containing the odd ball and divide it into 3 individual balls for the second weighing.

4. Weigh two of these individual balls against each other:

• If the scales balance, the odd ball is the one not on the scales, and you know its weight compared to the others.

• If one side is heavier, that individual ball is the odd one, and you can determine whether it’s heavier or lighter based on the previous weighing.

5. If needed, you can then identify the exact odd ball by comparing its weight to a known good ball using the scales one more time.


This method allows you to identify the odd ball and determine whether it’s heavier or lighter within two weighings.

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