• John Kador

A Puzzle. A Solution. An Experiment that Validates the Solution. Whew!

My Puzzler columns in REP, a magazine for financial advisors, have been popular for over six years. Many puzzles draw hundreds of responses. But I didn’t expect the enthusiasm that a puzzle I called “Odd Balance” published in November 2013 continues to generate.

To recap, You have a balance beam, the kind of scale that tips from one side to the other, depending on the weight on each side. On each side is a beaker, half-filled with water. The sides are in balance. Now, on the left side, you submerge a ping-pong ball suspended by a string. On the right side, you submerge a steel ball of the same volume as the ping-pong ball suspended from a crane. Does the balance beam tip to the right, to the left, or does it remain unchanged?

Which way will the balance beam tilt?

Which way will the balance beam tilt?

In the next few weeks my inbox overflowed with passionately argued solutions for all three conditions. Some people thought that the balance team would tilt left. An equal number argued that, no, it would tilt right. Still others thought the balance beam would remain balanced.

When I published the solution—the balance beam would tilt to the right because the displacement of water represented by the submerged steel ball weighed more than the weight of the ping pong ball and string—dozens of readers argued that my solution was wrong.

To such readers, I suggested they do the experiment and see for themselves.

I hardly expected anyone to take me up on the challenge.

But at least one reader did just that. Actually he enlisted his mother and father to do the experiment, videotaped it, and posted it on YouTube.

Joshusa Logsdon writes: “Our family loves puzzles, but this one was very compelling because of the many factors involved. The main discussion was between my two brothers who are both engineering students at Virginia Tech. They both adamantly disagreed, one arguing for no change, and the other (who is a senior) for the ping pong side being lighter. My mother, Ann Logsdon, is doing the experiment, and the voice in the background is my father, Ken Logsdon.”

Congratulations to the Logsdons for not taking my word for it and sharing the results. It means a lot to me that my puzzles are an opportunity for advisors, individuals and their families to enjoy putting their minds together.

For those who want more, this is the solution I posted explaining why the balance beam tilts right: On the left, the submerged ping-pong ball doesn’t change the weight of the beaker except for adding its own weight. The ping-pong ball can be set on the pan outside the beaker and have the same effect. On the right, the steel ball displaces water equal to its volume. That’s why the scale tips right. Here’s one way to think about it. Suppose the steel ball is suspended by a spring scale which registers, say, 5 ounces. Now, imagine slowly lowering the ball into the water. The weight registered by the scale will go down, but not to zero—maybe it’ll go to 3 ounces. That is, the water is supporting the ball somewhat, but not completely. That 2 ounces is additional weight adding to the weight of the beaker (in fact, that 2 ounces is the weight of a ball of water.)

In conclusion: on the left side, we have the additional weight of a ping-pong ball. On the right side, we have the addition of a ball of water. The right side is heavier and goes down, making the balance tilt to the right.

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