Hey Presto! - Futility Closet

A bit of conjuring adapted from Augustus de Morgan:

1. Think of a one-digit number and remember it. (Example: 4.)

2. Write down a number of any length. Jumble the figures into another number, and subtract one from the other:

de morgan

3. Count the letters in your father’s first name, your state capital, and the name of your favorite Beatle, and add them together.

4. Multiply this number by 4 and its reverse by 5. Add these together, plus the number from step 1.

For example, suppose your father’s name is William, your state capital is Oklahoma City, and you choose Paul. That’s 23 letters in all, and 23 reversed is 32. (4 × 23) + (5 × 32) + 4 = 256.

5. Mix these figures (256) into the result from step 2 (4600708659), in any order, say 4560207086569.

Seeing nothing but this final list of figures, the conjurer names the one-digit number from step 1.

How does he do it?

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The conjurer simply adds up the digits in the final figure. If the result has multiple digits, he adds those, and so on until he reaches a single digit: 4 + 5 + 6 + 0 + 2 + 0 + 7 + 0 + 8 + 6 + 5 + 6 + 9 = 58 5 + 8 = 13 1 + 3 = 4 That digit is the number from step 1. It works because all multiples of 9 eventually produce 9 when their digits are added as above; the procedure asks you to create two multiples of 9 (in steps 2 and 4) and to combine their digits and add your own. Adding the digits will thus yield 9 plus the number chosen (here, 13), and of course adding those digits will yield the number itself. The business with the father’s first name, etc., is just smoke — any numbers at all can be used in those positions. The arithmetic will always produce the right answer.

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