One of the trickier variations of a theme of logic questions.
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.
Show me the answer...
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.
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.
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.
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.