![]() We now replace 10 by the sum of its digits 1 + 0 = 1, so our “running total” is now 1 rather than 10. In the previous example, we would perform the following mental calculations: 1 + 1 equals 2, 2 plus 6 equals 8, 8 plus 2 equals 10. In general it’s faster (once you practice a bit) to keep a running total in your head as the digits are read aloud and cast out 9s as you go along. Let’s figure out the missing digit by casting out 9s:ġ + 1 + 6 + 2 + 1 + 6 + 0 = 17 and 1 + 7 = 8, so the missing digit should be a 1. (In algebra terms, if the missing digit is X, then X + 2 = 9 and therefore X = 7.)įor a larger, more realistic example, suppose the spectator reads the following digits out loud: 1, 1, 6, 2, 1, 6, 0. We know, however, that had the thought-of digit been included, we would have gotten a final answer of 9. Now 5 + 6 = 11 and 1 + 1 = 2, so by casting out 9s we obtain the number 2. Suppose we mentally circle the 7 and then read out the other two digits (5 and 6). What does this have to do with our trick, though? Well, take a look at the previous example of 756. It has a wealth of applications in real life, for example to error detection and correction through the concept of a check digit. Adding together the digits of a number, then adding together the digits of the result, and so on, repeating until we end up with a single digit is called casting out 9s. Note that this process can be repeated with 18, the answer we got from doing the previous calculation: 1 + 8 = 9. As another example, 756 is a multiple of 9 and 7 + 5 + 6 = 18. Principle #2: If you add together the digits in any multiple of 9, the result will also be a multiple of 9.įor example, 72 is a multiple of 9 and 7 + 2 = 9. There are actually two different principles at work here, and it’s the combination that I really love. The effect can be repeated again, if desired, by multiplying the random number showing on the calculator by some additional random digits and then going through the same procedure. And start counting out loud, slowly, from 1 to 9…” When she gets to 7 (say), the magician calls out “ Stop! That was it, wasn’t it - you were thinking of a 7!” The spectator confirms that she was. You can recite the digits from left to right or right to left, as you wish, but when you get to your mentally chosen digit, just skip over it and continue reading with the next one.” After the spectator has called out all of the digits except for the mentally selected one, the magician looks at her and says, “ Concentrate on your mentally chosen number one more time. The magician continues, “ I’d like you to read aloud all of the digits in the random number you’re looking at except for the one you mentally circled - just skip that one. “ Good… that one doesn’t work very well because it has no value.” “ You’re not thinking of a zero, are you?”, the magician asks. The magician asks the spectator to mentally ‘circle’ one of the digits in her number and concentrate on that digit. She is now looking at a completely random number having around 8 digits. This is repeated around 10 times in all, at which point the spectator hits “equals”. Then the spectator is asked to hit “times” (multiplication key) and type in another random digit from 1 to 9. The magician doesn’t look while this is happening. She is asked to open up the calculator and type in a single digit from 1 to 9. The magician asks a spectator to take out her cell phone. I claim no originality here, but I don’t know to whom proper credit belongs (see below for my best attempt at crediting)- it’s an old trick with numerous variations. ![]() It’s an especially practical trick at the moment, because it also works perfectly over Zoom. ![]() And while it might not be the most spectacular effect that I know, it’s actually quite deceptive and can be done completely impromptu. But nowadays just about everyone has a calculator on hand at all times on their cell phone. It used to be a bit impractical, because it requires having a calculator on hand. The following is a demonstration that I’ve been doing for decades. By Matt Baker - Wednesday, December 9, 2020
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