Weekly Maths (15) : Magic Number 9 11/04/2015

*

Magic number 9*

Think of any three digit number ABC

Rearrange it in different order eg. BAC

Work out the difference of the 2 numbers. 

You get xyz or xy

Remove one of the digit (except 0)from your answer, 

and show me the remaining digits.

 I will be able to tell the digit 

that you had removed.

Why? How?

Three different digits

*幻数 9* 

设想任何一个三位数的数字ABC 

以不同的顺序重新排列它，例如 BAC 

计算这两个数字的差。 

你得到 xyz 或 xy 

从您的答案中删除一位数字（0 除外）， 并告诉我剩余的数字。 

我将能够说出你已经删除了的数字。 

这是为什么呢？

原理何在？

*基本理论*

ABC-CAB=xyz

1.

ABC=9m+R

CAB=9n+R

xyz= 9(m-n) multiple of 9

2. 

ABC-CAB=(100-10)A +(10-1)B -(100-1)C

=90A+9B-99C

=xyz multiple of 9

3.

xyz multiple of 9

x+y+z= multiple of 9

4. 

ABC=9m+R

A+B+C= 9p+R