Puzzle Details: You are given 8 identical-looking balls. One of them is heavier than the rest of the 7 (all the others weigh exactly the same). You are provided with a simple mechanical balance and you are restricted to only 2 uses. Find the heavier ball.
Solution :
For convenience sake, let’s name the balls 1-8. First we weigh {1,2,3} on the left and {4,5,6} on the right. This is the first measurement. There are three scenarios that can arise from this.
Let’s consider the scenario1
If the left side is heavier, then we know that one of 1, 2, or 3 is the heavier ball. Now in the second measurement, Weigh {1} on the left and {2} on the right. By doing this, we will know if 1 or 2 is heavier. If they balance out, then 3 is the heavier one. In this case, the heavier ball is identified by exactly 2 measurements.
Let’s consider the scenario2
If the right side is heavier, then we know that either 4, 5, or 6 is the heavier ball. Now in the second measurement, Weigh {4} on the left and {5} on the right. By doing this we will know if 4 or 5 is heavier. If they balance out, then 6 is the heavier one. In this case, the heavier ball is identified by exactly 2 measurements.
Let’s consider the scenario3
If {1,2,3} and {4,5,6} balance out, then we know either 7 or 8 is the heavier one. Weigh both of them to find out which one is heavier. Again here heavier ball is identified by exactly 2 measurements.
Let's summarize: The first step is determining which set of three balls contains the heavy one. So choose balls 1,2,3 and balls 4,5,6 and weigh them. If one set is heavier, save those three balls. Pick 2 balls and place them for measurement By doing this we will know which one is heavier. If they balance out, then the other is the heavier one. If neither side is heavier in the first step, proceed with balls 7,8. In The final weighing Weigh both of them to find out which one is heavier.
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