Solution: Math Puzzle: Find the Heavy Ball

Leo can do it in two weighings. Here’s how:

1. Take any three balls and weigh them against any other three. There are two possible outcomes:
   A. they balance
   B. they don’t balance

Let’s pursue outcome A first. If three balls balance against another three, then the heavy one must be among the remaining three that are not on the scale. So, for the next step:

2. Take the six balls that were on the scale in step 1 and put them aside. Take two of the remaining three balls and put one on each side of the scale. If they balance, then the third one is the heavy ball. If they don’t balance, you’ve found the heavy one.

Now let’s go back to Step 1 and pursue outcome B. In this case, take the three balls that weigh in as heavier and proceed to Step 2 using them.

In either case, it takes just two weighings to isolate the one heavy ball out of nine. Leo can now proceed up the tower to drop the two balls. Of course, he is very careful about safety and will make sure there is no one below before he releases the balls.