## Friday, 10 February 2017

### Introduction to Algebra... Crystal Ball Gazing...

Could you UNCOVER THE MYSTERY behind the crystal ball?
(in the Algebraic way!)

1. Multiply 9 with the first digit.

2. The flash mind reader works with multiples of 9, so all the multiples of 9 is the answer, from 9 to 81, but they are mixed up every time so as to confuse us.

3. This comment has been removed by the author.

1. Do you mean 9x?

2. This comment has been removed by the author.

3. Number in tens place is x
Number in ones place is y
The number =10x+y
10x+y-(x+y)=9x
so the answer is always a multiple of 9

4. @Zun Kye
Clear explanation :)
5 points for group 4

4. If n = 82
82=8x10+2
=8a+2b
10a+2b-(a+2b)
=9a
Therefore, the numbers is a multiple of 9

1. if you put 8x10+2=8a+2b, it will seem like a=10 and b=1 because 8x10+2=8x10(a)+2x1(b).

2. The answer will still be the same

3. @Ethan
The 3rd line of the working, when generalized (using your example) would be 10a+b
So that it can represent any 2 digit number.

5. All answers are multiplication of 9 hence taking the number in tens as a and number in ones are b, 10a+b, subtract a+b=9a