Tim Pennings: Mathematics in the sauna
At the gym, I find not only a great break from Michigan’s cold winter, but also some great conversations.

This time of year, I make good use of my Priority Health (Medicare) free admission to MVP and the Holland Aquatic Center. The main course for a good workout is some aerobics and weightlifting, and the dessert is the sauna and whirlpool. But, as the saying goes, “Life is short – eat dessert first.” So I sometimes bypass the workout (since my opportunity as a professional athlete is lessening daily), and head straight for the reward.
And there I find not only a great break from Michigan’s cold winter, but also some great conversations. It’s the non-coffee-drinker’s substitute for LemonJellos. Sometimes conversations happen spontaneously. Recently, asking a couple young fellows if they were in college, they responded that they were in a Leadership Bible class. This led to a six-way conversation among all the occupants about all things scriptural (complete with memorized verses and references). I was concerned when new people entered the sauna that they would be overwhelmed by the conversation, but, (much to my surprise – but perhaps it shouldn’t have been) the newcomers jumped right in with their own opinions and scriptural references. Only in West Michigan!

However, if no conversation is forthcoming, then, as I did last evening with a Black River sophomore, I ask if they want to play a math game. Haven’t been turned down yet. My favorite is “Don’t say 21.” Here are the rules. Two players take turns counting from 1 to 21. Starting at 1, they alternate, each counting the next one, two or three consecutive numbers. So, for example, if I start by saying “one, two,” then my opponent may say “three” or “three, four” or “three, four, five.” Then, starting where he stopped, I say the next one, two or three numbers. Whoever is forced to say “21” is the loser.
Try it with a fellow nerd and see who can be the first to discover the strategy to win. Hint: If both players know the strategy, then the second one to play will always win. (Solutions at the end, but don’t spoil the fun — try to figure it out first.)
Here’s another one: Using a belt, strap, or shoelace, or even a towel if necessary, lay it C-shaped in front of you. Then, picking it up, one end firmly in each hand, tie a simple under-over knot in it between your outstretched hands WITHOUT LETTING GO OF EITHER END.
By the way, these challenges work well even outside of a sauna. They are great ways to entertain children or grandchildren around the holiday table. Indeed, I give math talks in which I demonstrate these and others. All promote creative thought and tenacity — two essential ingredients for success in many careers and life in general.
Here’s another: Using six coins (or other small uniform objects), place them in the form of a cross with four in the vertical row and three in the horizontal row, so that a line passes over four coins in one direction and three coins in the other direction. Challenge them to move one coin so that a line passes over four coins in one direction AND four coins in the other direction as well.
Another: Position a rubber band (an elastic hair band can almost always be found on the sidewalk entrance to an athletic club), around the base of your index and middle fingers of your clenched hand. Then by quickly opening your hand, the band is instantly transferred to your ring and little fingers.
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Solutions: “Don’t Say 21”: Notice that for my opponent to lose, I must say 20. In order to guarantee saying 20, I need to say 16. To guarantee that, I must say 12, then 8, then 4. So 4, 8, 12, 16, 20 are safe lily pads from which to jump. Try it. If you go second, you will always be able to say those numbers.
Knot in Belt: The trick is to transfer a knot in your arms to a knot in the belt. So first cross your arms into an over-under knot, and then, bending over as needed, pick up the ends of the belt. Then merely untie your arms, and the knot will transfer to the belt.
Six Coins: Notice that the coin at the intersection of the rows counts twice. So just place another coin from the vertical row ON TOP OF the coin at the intersection.
Last one: I’ll show you when I see you in the sauna. Have fun.
— Community Columnist Tim Pennings is a resident of Holland and can be contacted at timothy.pennings@gmail.com. Previous columns can be found at timothypennings.blogspot.com.