Question: 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 a provided with a simple mechanical balance and you are restricted to only 2 uses. Find the heavier ball.
Answer: For convenience sake, let’s name the balls 1-8.
Step 1 : First we weigh {1,2,3} on the left and {4,5,6} on the right. There are three scenarios which can arise from this.
Scenario 1 / Step 2
If the left side is heavier, then we know that one of 1, 2 or 3 is the heavier ball. 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.
Scenario 2 / Step 2
If the right side is heavier, then we know that either 4, 5 or 6 is the heavier ball. 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.
Scenario 3 / Step 2
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.
So we got the solution in 2 steps.
Answer: For convenience sake, let’s name the balls 1-8.
Step 1 : First we weigh {1,2,3} on the left and {4,5,6} on the right. There are three scenarios which can arise from this.
Scenario 1 / Step 2
If the left side is heavier, then we know that one of 1, 2 or 3 is the heavier ball. 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.
Scenario 2 / Step 2
If the right side is heavier, then we know that either 4, 5 or 6 is the heavier ball. 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.
Scenario 3 / Step 2
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.
So we got the solution in 2 steps.
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