Can you find the sum??

Number Theory Level 3

What is sum of all four digit numbers formed by using the digits 0 and 1any number of times and divisible by 11.


The answer is 3212.

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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2 solutions

Rama Devi
May 16, 2015

The only such numbers are 1001 , 1111, 1100. Therefore the sum of these digits is 3212.

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Ankit Kumar Jain
Mar 20, 2015

You can easily get 4 digit numbers made entirely of 0 and 1 :

1111 , 1110 , 1101 , 1100 , 1011 , 1001 , 1010 , 1000

Out of which 1111, 1100 and 1001 are divisible by 11.

So S u m = 1111 + 1100 + 1001 = 3212 \boxed{Sum = 1111 + 1100 + 1001 = 3212}

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