Stop writing 1's!

Number Theory Level 2

$\large \underbrace{1111111\ldots1}_{\text{number of 1's }=\, n}$

I pick a positive integer $n$ at random between 1 and 1000 inclusive, and then write up the number above.

Is this number more likely or less likely to be divisible by 11?

It is more likely It is less likely It is equally likely

1 solution

Guilherme Niedu
Jul 7, 2017

It is easy to see that if $n$ is odd, the number will be divisible by $11$ , and if $n$ is even, it won't be divisible by $11$ . So, equally likely.

Does this work for all odd /even "n"s? Why?

Pi Han Goh - 3 years, 11 months ago