Problem:

 

 

 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. 

 

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. There are three scenarios which can arise from this:


1) If {1,2,3} is heavier:

Then we know that one of 1, 2 or 3 is the heavier ball.

Put {1} on the left and {2} on the right.

If the are equal, {3} is the heavier ball.

Else, by weighing we can figure out if {1} or {2} is heavier.


2) If {4, 5,6} is heavier:

Then we know that one of 4, 5 or 6 is the heavier ball.

Put {4} on the left and {5} on the right.

By doing this we will know if 4 or 5 is heavier.

If they have the same weight, then 6 is the heavier one.


3) If {1,2,3} and {4,5,6} balance out, then we know either 7 or 8 is the heavier one.

By weighing {7} on the left and {8} on the right, we can figure out which one is heavier.

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