## Saturday, 22 February 2014

### 6 AM Quiz: Let's Test FIDO out!

In this round of 6 am quiz, you will attempt to uncover the mystery behind Fido's Mind-Reading ability.

Fido claims that he can read our mind.
Click at the following link to test him out!!! :
http://www.digicc.com/fido/

There are several ways to explain Fido's trick, using mathematical reasoning.
Make an attempt to use ALGEBRA to explain the "trick"?

1. Okay....
I chose 4615 and made another which is 5164.
I subtracted both of them and out with 549.
I circled 5 and wrote 94 on the screen.
Surprisingly, Fido gave the missing digit, 5!!!

Fido's point of view:
Digit 4 and 9 is given.
Let the missing digit be 'x'.
Possible numeral patterns are...
- 100x+40+9
- 100x+90+4
- 400+10x+9
- 900+10x+4
- 400+90+x
- 900+40+x

Fido knows that the answer is always divisible by 9.
Fido chooses one possible pattern: 900+40+x
Possible value of x is 1,2,3,4,5,6,7,8,9.
So...
941 divided by 9= NOPE
942 divided by 9= NOPE
943 divided by 9= NOPE
944 divided by 9= NOPE
945 divided by 9= YES!
945 is divisible by 9.

So the missing digit is 5!!!

1. Phew...
That was hard~
Is it right, Ms Loh?

2. @Gijoo
Hope that you find this interesting and has challenged you to think deeper :)
That's the 'magical' touch that algebra gives :)

Cheers!

3. The answer is correct. Its very interesting and in depth. Good job Gijoo!