01 November 2004
Let Us Be Logical
Let's say you're at the edge of a forest that you have to walk through in order to get to a safe place to sleep on the other side. You've heard that there's a tiger that's been attacking and eating travelers along a path in the forest. There are four paths in front of you, each one with a sign indicating that it leads to your destination. Which do you take? You figure you have three chances out of four that the path you choose will be safe, so you pick one and set off into the dark forest. What you can't see is that the two on the left will eventually merge into a single path, and the two on the right into a second path. Then, those two paths will merge into a single path, and it's along that path that the tiger's lurking. So, of course, the tiger attacks and eats you.
Magic tricks, like the one at the top of this page, depend on things not being what they seem. The illusion in this trick is that you have choices from among many different possibilities, and since you keep your choices a secret it would be virtually impossible for anyone to guess any of them, let alone all. In fact, to someone who knows how the trick works all your choices are about as predictable and inevitable as the tiger lurking along the path.
Your initial choice is between ten options, the numbers from 1 to 10. Obviously, someone would stand only a one in ten chance of guessing which number you choose, but your choice makes as little difference as your choice from among the four paths through the forest. Let's say you pick 1. If you multiply 9 by 1 you get 9, obviously. If you picked 2 you'd get 18, a number consisting of two digits that add up to 9. You can see that from then on, whatever number you choose, when you multiply it by 9 the first digit will go up by one and the second digit will do down by one: 27, 36, etc. That's just a fact about the number 9 and the decimal counting system.
So for the first part of the trick, it's just an inescapable mathematical fact that you'll get the number 9 after the first two operations. Then, you subtract 5 from 9 to get 4. No initial choice could possibly yield a different number.
From then on, it's possible that different people will make different choices, but it's unlikely. Since the first part always leads you to 4, it always leads you to D when you do the number-letter conversion. There are only three countries in the world that start with D: Denmark, Djibouti, and the Dominican Republic. If you come from Djibouti or the Dominican Republic, the trick would get loused up at this point, but for reasons of political and cultural accident most people are going to be more familiar with Denmark than the other two. Most Americans probably don't even know Djibouti is a country. Then, you get E, and once again the next step depends on the cultural fact that most people are going to think of elephant rather than, say, eel, emu, or echidna. That greatly reduces the chance that someone will pick the "wrong" animal. That takes you to the color gray, and the explanation for kangaroo is the same as for elephant. That takes you to O, and the choice of orange is the same as the explanation for elephant and kangaroo. What other fruit starts with O?
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