Which ball is heavier?
Imagine you have nine balls and a scale.
The balls look exactly the same, but one of them is actually heavier.
How do you determine which ball is the heavy one by using the scale only TWICE?
Solution:
1) Take six balls and split them into two groups of three. Put each group onto one dish of the scale. (One set of three should be left lying around somewhere)
Here are the possible scenarios:
- Left side gets dragged down. Heavy ball among the left.
- Right side gets dragged down. Heavy ball among the right.
- Both sides are balanced. Heavy ball among those that are not on the scale.
Whatever you do, you end up with 3 balls where the heavy one is among one of them.
2) Take the three balls (the group containing the heavy one) and do a similar procedure:
Put two on the scale, and leave one on the table.
The heavy ball will either be on the scale weighing one side down, or on the table because both sides are balanced.
That's it!
