### Chap 4: Algebra... Crystal Ball Gazing...

Could you UNCOVER THE MYSTERY behind the crystal ball?

1. Well, since you did go through in class but i'll give it a go.

Example:
any two digit number. i pick 10.
1+0= 1
10-1=9 ( which is 1 x 9 )
I see the picture and click the crystal ball. my picture is correct.

Example 2:
I pick 30.
3+0=3
30-3=27 ( which is 3 x 9 )
I see the picture and click the crystal ball. my picture is correct.

Example 3:
I pick 44.
4+4=8
44-8= 36 ( which is 4 x 9 )
I see the picture and click the crystal ball. my picture is correct.

From the results i can conclude that the mystery is simple. the numbers can only be two-digit. not one-digit nor three-digit. so the pictures and answers i've shown above are all multiples of nine, thus i can say that the "sum" of two digit numbers has been made such as all answers lead to multiples of nine.

2. Lets say from the numbers 10-19

all the numbers ( accoding to thier steps) will result in the same answer nine. Notice the symbol of nine.

All the numbers from 20-29 will result in the number 18

All the numbers from 30-39 will result in the number 27

All the numbers from 40=49 will result in the number 36

All the numbers from 50-59 will result in the number 45

All the numbers from 60-69 will result in the number 54

All the numbers from 70-79 will result in the number 63

All the numbers from 80-89 will result in the number 72

All the numbers from 90-99 will result in the number 81

Notice that they are all multiples of nine, and all of these numbers will result in one symbol.

To confuse you, every time the game reloads, they change the symbol of these multiples, just to make the mysterious feeling.

3. Grace and Calvin

These are good attempts :D
Hm... Using the listing method, you are able to present 'specific' cases that are true within the range of numbers (i.e. 2 digit numbers).

Perhaps the next level of challenge is, to generalise the specifics.

How do we use algebra to help us explain the operations behind the mystery?

:D