Comments on: Math Magic: Mind-Reading in Person

By: ashley

ashley — Tue, 12 Aug 2008 18:22:07 +0000

wow that was so cool

By: Ξ

Thu, 13 Dec 2007 16:10:32 +0000

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!

By: Ξ

Sat, 01 Dec 2007 11:02:10 +0000

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…..