Process

**II. Assignment**
 * Great Job ! ! [[image:girl_with_birds.gif]]**

[|**http://www.cut-the-knot.org/Curriculum/Magic/MindReaderNine.shtml**]
 * Check the following web page in which you have a magic trick.**

1. Read the instructions, cut them and paste them to your wiki.** ** __Underline__ ****the words that are time markers.** Think of a 2-digit integer. Subtract from the number the sum of its digits and find the result in the table below. Note that each cell of the table contains a number and a geometric shape. Concentrate hard on the shape that shares a cell with the result of your calculations. __When__ ready, press the "Check it!" button ... ** **Good** Well, when I played the first time, it surprised me. But after I noticed that all result **S**  had been zero or multiple **S**  of nine, until eighty-one, and the shapes were the same. **Good**
 * Follow these steps:
 * An Arithmetic Magic Trick
 * 2. Play and try to explain why the magic trick worked.**

I thought about something similar, but I did not thought in the algebraic part of the problem, where AB is a number, and it can be written on base ten as (A * 10 ^ 1 + B). Later AB = ((A * 10 ^ 1) + B) - (A + B) = A10 +B - A - B = A10 - A = A9 = 9A. This is an excellent way to see it. **Good**
 * 3. Check the explanation below the trick. Was it the one you were thinking of? Explain.**

Answer: This is because when you have a whole number and this is the absolute value remains the same, the result will always be a multiple of 9. The figures of the multiples of 9 will always be the same.