Find the Heavy Ball

Can you duplicate Galileo's experiment?

Leo Galley wants to duplicate the famous experiment in which Galileo dropped two iron balls of unequal weight from the Leaning Tower of Pisa to verify that they fall at the same rate. You can check this for yourself at Galileo Drops the Ball [1].

Leo has nine balls, all of the same size. Even though they all look alike, he knows one of them is heavier than the rest. He wants to take the heavier one, along with one of the others, up to the top of the Leaning Tower of Pisa and drop them both off.

He has a balance with which to weigh them against each other.

What is the smallest number of weighings he needs to find the heavy ball?

[1]

Course:

Math [2]

Result/Solution(s)

Solution: Find the Heavy Ball Math Puzzle

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

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:

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.

math [3]
Math Puzzle [4]