Math Magic: Mind-Reading in Person

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crystal.jpgHere’s a little mind-reading trick to amaze your friends and family!

Ask for a volunteer. The volunteer should pick a number; the number of digits doesn’t matter, but a 4-digit number tends to be big enough to be impressive without being overwhelming. The volunteer should write the number down, but not show you what it is. For example, the volunteer might secretly pick 2748.

The volunteer should then scramble the digits of the original number, find the difference between the original number and the scrambled number, and write down that difference. For example, if the scrambled number is 8247, then the difference would be 5499 (which is 8247-2748).

The volunteer then circles one of the digits in the just-obtained-difference, except it’s forbidden to circle the digit 0 (because 0 is already a circle, you can explain if asked). The volunteer then takes the remaining digits, writes them down in any order for the final number. For example, if the volunteer circles one of the 9s in the number above, then the final number would be 5, 4, and the remaining 9 in some order, like 495.

The volunteer then shows you this final number, and from that you are able to determine the digit that was circled! Amazing!

Want to know how to do it? It actually uses a similar trick as the websites on yesterday’s mind-reading post. We’ll post the answer as a Comment in a few days; in the meantime, you can play the game here on the computer (click on the guy in the lower left-hand corner of that site to get started).

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3 Responses to “Math Magic: Mind-Reading in Person”

  1. Ξ Says:

    Here’s the Big Hint: whenever you take the difference between two numbers with the same digits (so one is a permutation of the other), the result is a multiple of 9. So 8247-2748 would be a multiple of 9.

    There are several ways to prove this. One indication of how a proof could be constructed is to break each number into its components (8000+200+40+7) – (2000+700+40+8) and then look at each digit: 8000-8 is 8*(1000-1), which is 8*999 [clearly a multiple of 9]. The 200-2000 simplifies to 2*(100-1000) or 2*(-900) which is also a clear multiple of 9. The 40-40 is 0, which is a trivial multiple of 9, and the 7-700 becomes 7*(1-100) or 7*99.

    (Different numbers will of course give different results, but it does turn out that the result that you get will always be a multiple of 9).

    Another hint will follow later…..

  2. Ξ Says:

    Here’s another hint: When a number is a multiple of 9, its digits must add up to a multiple of 9. For example, 54 is a multiple of 9 and 5+4=9. The digits of 3489507 add to a multiple of 9 (3+4+8+9+5+0+7 = 36) and sure enough 3489507=9*387723).

    This is the fact you use to figure out what number was circled. It’s also why there would be confusion over circling 0 (in particular, you wouldn’t be able to tell if a 0 or 9 had been circled).

    Post in the comments section if you need any further hints!

  3. ashley Says:

    wow that was so cool

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