Go see The Flash Mind Reader. It’s pretty cool. It really works.
But how does it work?
The instructions say to “Choose any two-digit number, add together both digits and then subtract the total from your original number.” There must be something common to all of these answers. Let’s find out.
Warning: Math ahead! (But it’s not that bad, I hope.)
Lets represent any two-digit number with:
10a + b
where a is the tens digit and b is the ones digit. For example, if we use the number 73, then a=7 and b=3, and 10*7 + 3 makes 73. Remember in grade school where you learned the place values of the digits in a number, like thousands, hundreds, tens, ones? Algebraicly, that means 1000w + 100x + 10y + 1z.
To add the digits together becomes easy:
a + b
Now to subtract this from the original number looks like:
10a + b − (a + b)
Distributing the negative sign:
10a + b − a − b
Leaves us with:
In other words, whatever two-digit number you originally pick, it does not matter what the ones digit was. Only the tens digit matters and it will get multiplied by 9. This means that the answer of this process will always be a multiple of 9.
Looking back at the table of numbers and symbols, notice how all the mulitples of nine (9, 18, 27, …) have the same symbol? This is the symbol that will appear in the crystal ball.