Math-magical thinking

Click on the name of this post, Math-magical thinking, and it will take you to a web page that will amaze you.

Do not read any more of this posting without examining the page and trying it out.

Surely it is magical!

Now let's do the required numerical thinking, not to diminish the magic of the webpage I sent you to, but to increase the magical-ness of math.

Any two digit number has two digits, call the first "x" and the second "y". When we place them together to form a two digit number, as in "xy", the value of the number itself is 10x + y. This is the difference I referred to in an earlier blog, the differnece between a number, and the quantity it represents. (Not all numbers do that, by the way)

"82", for example, is ten 8's + 2. Similarly "xy" is ten x's + y. We write that 10x + y.

So you made up a two digit number with the value 10x + y.

The puzzle now asks you add the two digits together. That give us a second number, x + y.

Finally you are to subtract the second number from the first, giving:

(10x + y) - ( x + y)

When you simplify that expression you are left with 9x. In other words, no matter what two digits you choose to use, once you perform the steps outlined, your final answer will be exactly 9 times larger that the digit you used for x, the digit in the tens place.

Which means that every possible answer is a multiple of 9. To whit 9, 18, 27, 36 and so on. No other answers are possible.

If you go back to Math-magical thinking link, look to see what symbols go where, and in particular notice the symbol matching multiples of 9.

That's math-magical thinking. Math is very, very cool.