Categories

# How do you do the disappearing coin trick?

This isn’t really magic, and probably a very inefficient process. We only think, because we use the mathematical formula for hidden letter frequencies.

Suppose we set up some very fast computers to run our method, and each of us just asks him to answer the questions, one at a time. All the questions we ask is how many letters of a word there are in a word. So it’s easy to ask the computer, “how many times does a string x occur in the phrase `one thousand one pound’? Well that’s easy!”

You know from the above, that when we have a “string” that’s just a bunch of letters, we’ll often get a word consisting of a letter, a short vowel or an apostrophe, some dashes, or some consonant. There are many ways to generate that word.

Here’s a trick, though…

Here’s how we know the answers we get to our questions:

1) We’re very good at using our computers to solve problems.

2) The computer will have the same answer for us, every time.

3) The computer answers our questions quickly — and sometimes much more quickly than us. You can look at the time it took to answer our question from the beginning, and then compare it to the time it took us to look up the answers in a spreadsheet or elsewhere.

For example, take the letters of this phrase “one thousand one pound”: They’ve all been searched up, in the first half-second of running the computer for over a minute. The “s” on that letter has been searched up about eight times. The same is true for some other letter, depending on whether you’re looking up the last word in the phrase, or just looking up the word you’re after. But it only takes us half a second for the computer to have found the whole word “one thousand one pound”. That’s why we get back “one thousand one pound” each time. Now how does that figure add up to the entire phrase with those five letters? It doesn’t. The last letter that we look up has only happened twice in the whole phrase.

Why is that?

Well, we were really good at looking up the first part of the phrase. Here’s our answer: “one thousand pound”. Our second answer… “one thousand thousand one pound”. Our first answer would be the number of the longest word in the phrase. Our last sentence,