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TheMagicianGuide New user Wheat Ridge Colorado 90 Posts |
Ok, this even amazed my wife (its hard to amaze her much anymore, haha)
9 x any number. (any whole number that is) so lets say 9 x 348 = 3132 Add together the digits in the answer: 3+1+3+2=9 The sum will always be 9 or a multiple of 9 . . . it really is simple, but fun. Doing this on a calculator with kids is pretty good too . . .
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
More generally, the remainder when you divide a number by 9 (or 3) is the same as the remainder when you divide the sum of that number's digits by 9 (respectively, 3).
This is a well-known result in number theory. Without going through the full proof, I'll mention that it stems from the fact that the base of our number system - 10 - has a remainder of 1 when divided by 9 or 3; the same holds true for 100, 1,000, 10,000, and, indeed, any nonnegative power of 10. |
The Magic Cafe Forum Index » » Magical equations » » An easy one . . . 9 x any # . . . (0 Likes) |
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