# Three-digit numbers

May 1998

A three-digit number is such that its second digit is the sum of its first and third digits.

**Prove** that the number must be divisible by 11.

May 1998

A three-digit number is such that its second digit is the sum of its first and third digits.

**Prove** that the number must be divisible by 11.

## Comments

## proof 3digit

Let digits are a,b,c

Let b=a+c because second digit is sum of last and first

So number=a*100+b*10+c*1

=a*100+(a+c)*10+c*1

=a*100+a*10+c*10+c*1

=110*a+11*c

=11*10*a+11*c

=11*(10*a+c)

That is the number is multiple of 11 so it is divisible by 11

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## three-digit numbers

All right, but how can you prove that a number like 62345678987654555548 (or even a bigger number) is divisible bij 11?

## yes...

yes.

1 way: Use calculator for windows 7, which is totally capable of numbers larger than that.(12 digits longer than 62345678987654555548)

the other speedy way:

What is:

6 - 2 + 3 - 4 ...?

If it is 0 or 11 or -11, it is divisible...

if it isn't, no.

## Yes

It can be done with 121 1+1=2 and 121 is divisble by 11