As a math teacher, I like to perform several math tricks for my students, as well as friends and family. Many common tricks are based on properties of integers, and order of operations. These are nice, but can become stale after awhile. I have an all-time favorite trick, which I wish to share with you now.
I first saw this trick performed by an amateur magician. The crowd was amazed by the performance. I was not. I knew how it was done. To the observer, the trick is performed first, when the magician asks a member of the audience to pick a letter of the alphabet, and share with the group. The magician, not knowing what that letter is, grabs a set of five cards, or sheets of paper. On each card are several letters of the alphabet. The magician asks the volunteer if the letter is on each card. Based on the response, the magician can tell what letter the participant had thought of.
Most people will not realize just how simple this math trick is. To understand it, first consider how many combinations of "yes" and "no" are possible. If you did your math correctly, you will realize that there are 2x2x2x2x2 or 32 total possibilities. How many letters are in the alphabet? All the magician needs to do, is have a key representing the different combinations, and the corresponding letter.
I made my sheets using the following steps. First, I chose to use a binary system to represent the audience response of different letters. For examples, 10101 would stand for, "yes," "no," "yes," "no," yes." Each letter is assigned a unique binary representation. I like to avoid 00000 and 11111, as both of these represent all yes, or all no. Once all letters have been assigned, I write each letter with a 1 in the first digit on the first card. Then I write each letter with a 1 in the second digit on the second card. Repeat through card number five. I like to write the letters randomly on these cards, so as not to give away that there is some sort of logical reasoning for their placement. On the back side of the fifth card, I write my key, with each letter and its corresponding binary number. I write it small and light, so it's not obvious that it's there. I practice a few times to make sure I did not make any mistakes, and then it's ready for public display.
This trick is simple to do, and has excellent replay value. It can be used to help students or others understand binary numbers, combinations and permutations, powers of two, or simply to amaze.