Saturday, February 20, 2016

365 True Things: 328/Math

In high school, I enjoyed algebra but not geometry. I loved trigonometry, though I can't tell you what it's actually used for. Maybe I mostly loved using the trig tables: it was like hunting for and assembling pieces of a treasure. In college, I took some calculus: the first semester was all equations, and I did fine there; the second semester was all word problems, and I failed miserably. No one ever taught me how to solve word problems—that is, how to analyze the scenario presented and translate (because it is a matter of translation) the words into equations! Word problems are not intuitive, at least not for me.

I was reminded of this today when I set about solving a "puzzle cache" called "The Man Who Counted." Here's the story (the word problem, as it were), abbreviated:
A ship's captain places between 200 and 300 gold coins in a chest to reward three brave sailors when they return to port. During the night, though, one sailor steals into the room where the chest sits, divides the coins into three piles, and takes his third of the total. One coin is left over, which he throws overboard. The next night, the second sailor does the same thing, followed the next night by the third sailor—both times with a remaining coin being tossed overboard. When the ship docks, the captain takes the chest with the remaining coins to an accountant, who divvies the coins into three piles—and keeps the single leftover coin for himself.
What we need to find is the total number of coins that were placed in the chest originally and the number of coins the first sailor ended up with. These numbers will then be plugged into geographical coordinates to reveal the cache's location.

My calculations for
"The Man Who Counted"
I sat and puzzled over the problem for, oh, about five minutes (patience is not my long suit, especially when it comes to anything more mathematically complicated than balancing my checkbook), then turned to the resident math professor for help. He patiently steered me, and steered me some more, and yet some more. (He also reminded me about the equal sign and working from one statement to the next. I was trying to treat the equations like sentences that needed heavy editing. This did not please the math professor.)

I finally got the answer, and he assured me that I had solved the problem. But it felt a little like those chin-up machines where you can lower the resistance in order to minimize the effort required: you dial in zero resistance and then feel virtuous for doing ten chin-ups. I did not feel virtuous, and I'm not sure I could repeat the process at even 50 percent resistance. (I should probably try. It might be good for me.)

Still, I got the coordinates (though not at first: I'd forgotten one key element in my calculation), and shortly thereafter we went out and found the cache. Victory!

I actually like puzzle caches—especially this particular cache owner's: he's smart and tricky, plus he makes up amusing little stories to go with, about a certain Humphrey Cutherburton Montesque Smythe. Puzzle caches certainly tickle the brain cells. Maybe they're the lazy just-want-to-have-fun equivalent of trigonometry. I keep hoping they will teach me a little more persistence and patience, but so far that's only wishful thinking.

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