## Saturday, 18 February 2017

### 6 AM Quiz #03b: Let's Test FIDO out!

NOTE: This week, there are 2 quizzes. The following (2nd quiz) rides on similar concept as the CRYSTAL BALL. Have FUN (even if you are not solving the puzzle).

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"?

Have Fun!

1. For example, if I choose 674 as my number, a = 100, b = 10 and c = 1
So, 674 = 6a + 7b + 4c
If I jumble up the numbers to be 467,
467 = 4a + 6b + 7c
674 - 467 = 2a + b - 3c
So, 674 - 467 = 200 + 10 - 3
= 207
= 2a +0 + 7c
No matter what, all the coefficients will add up to 9.
So for example, if I circle 2 and put in 0 and 7, the computer would take 9 - 7 - 0 and find out the answer which is 2.

2. If I use the number as 9999 then I jumble it up and still get 9999, 9999-9999=0 then I cannot circle anything but the answer says 9
But if I choose 976 and I jumble the numbers to get 679, 976-679=297 then I circle 7, 9-2=7 so the computer will say 7
And if I jumble the numbers to get 769, 976-679=207 and if I circle 7, 9-2=7 but if I circle 2, 9-2=7.
So the computer will always minus the numbers that you entered by 9, except for the nines that you entered
using the first paragraph, 9-0=9 so the computer gives 9

3. Using algebra,
I use the number 6754.
6=a 7=b 5=c 4=d
I transform it to 5476
5=a 4=b 7=c 6=d
6754-5476=1278
1a+2b+7c+8d
I take away the number 2, add 1+7+8=16
So,1=x 7=y 8=z
1+2+7+8=18
18-(x+y+z)=2