Nice

[lzy960601]

Nice

[XilaiZhang]

For question 2 beautiful numbers, I wrote a short proof of why our objective function is monotonically increasing

[XilaiZhang]

forgot to mention, the above is about 2016 round E question 2 beautiful numbers.

[lzy960601]

Sorry, but I think your code returns the wrong answer on input N = 269 and N = 585.
My solution is, N = 1 + B + B^2 + ..., so B must be a factor of N - 1, and we can enumerate all of the factors of N - 1 to find the best one.
@XilaiZhang

[XilaiZhang]

based on runs from yesterday and today the answers seem to be correct:

Here are runs on google kickstart environment:

And i think you are trying to verify result for 259 instead of 269?

[lzy960601]

Ah, sorry for that, I ran your code in a wrong way. Nice work!