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ASK Dr. RICH!
Rich Simons | 11th Street

 

Q: What is your favorite way of relaxing? – b.a.

Certainly, after a long, hard day of solving all the world’s problems, I need to “unwind.” What I like best is to curl up in front of the old fireplace with a glass of chardonnay in my hand and something from one of my favorite authors, Allan Gottlieb – editor of the Puzzle Corner in MIT’s magazine Technology Review. His works are a constant source of comfort, as I think you will discover in the following excerpt:

“A medallion hangs from a 30-centimeter (weightless, frictionless, etc.) string that is attached asymmetrically to the wall, one end at (x,y) = (0,0), the other end at (15,-12) (coordinates are in centimeters). With the medallion at its equilibrium position, the string will form a lopsided V. Find the (x,y) coordinates of the point on the string from which the medallion hangs.“

In his more lyrical passages, his prose glides along like a series of high, puffy clouds:

“Suppose there are four dice: Blue, Green, Red, and White. These dice have different numbers than usual printed on their six faces. After observing a long sequence of experiments rolling pairs of these dice, you conclude the following:

- When both are rolled simultaneously, the blue die gives a higher number than the green die two-thirds of the time.
- When both are rolled simultaneously, the green die gives a higher number than the red die two-thirds of the time.
- When both are rolled simultaneously, the red die gives a higher number than the white die two-thirds of the time.

You are now asked to consider rolling the blue and white dice simultaneously. What can you conclude about the probability that the blue die will produce a higher value than the white one?”

But just when you have relaxed and think you know where his narrative is going, Gottlieb will challenge you to decipher his true intent:

“What size cube has the same number of square inches in its surface area as it has cubic inches in its volume? What about spheres?”
And send you on a search for even deeper meanings:
“How many integers from 1 to 100 can you form using the digits 2,0,1, and 3 exactly once each.; the operators +,-,x (multiplication), and / (division); and exponentiation? We seek solutions containing the minimum number of operators; among solutions having a given number of operators, those using the digits in the order 2,0,1,3 are preferred. Parentheses may be used; they do not count as operators. A leading minus sign, however, does count as an operator.”

So if it is a long evening of relaxation you are after, I can definitely recommend a roaring fire, a wine of your choice, and Gottlieb. You will be asleep in no time.


 

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