Balls and Scales
One of the trickier variations on this problem.

One of the trickier variations of a theme of logic questions.

Question
You may be asked to explain your thinking as you work through the question.

You are given 8 balls. Seven balls have the same weight. Just one ball is heavier than the rest. Using weighing scales, find the heavier ball in as few steps as possible.

Answer

Start

Let's label the balls 1,2,3,4,5,6,7,8

Put balls 7 and 8 away. Weigh balls 1,2,3 against 4,5,6.

Case 1

The scales match. Balls 1,2,3 weigh the same as balls 4,5,6

Clearly none of 1,2,3,4,5,6 are the heavier ball.

Weigh 7 against 8 to find the heavier ball in 2 turns.

Case 2

The scales do not match. Suppose 1,2,3 are heavier than 4,5,6.

Take any 2 balls from 1,2,3 and weigh them.

It should be clear which is heavier, again using 2 turns.

The Answer

CLearly, we can find the heavier ball in 2 turns.

But what about if one ball was heavier OR lighter. What then ?

Take a look at some of the other variations on this theme to see why you might not see the wood for the trees.