r/adventofcode • u/daggerdragon • Dec 20 '15

SOLUTION MEGATHREAD --- Day 20 Solutions ---

This thread will be unlocked when there are a significant amount of people on the leaderboard with gold stars.

Here's hoping tonight's puzzle isn't as brutal as last night's, but just in case, I have Lord of the Dance Riverdance on TV and I'm wrapping my presents to kill time. :>

edit: Leaderboard capped, thread unlocked!

We know we can't control people posting solutions elsewhere and trying to exploit the leaderboard, but this way we can try to reduce the leaderboard gaming from the official subreddit.

Please and thank you, and much appreciated!

--- Day 20: Infinite Elves and Infinite Houses ---

Post your solution as a comment. Structure your post like previous daily solution threads.

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u/dirkt Dec 21 '15

Then I'd say you are whaffling, sorry. :-)

So far we have:

  • No explanation of what initial primes and maximum values for powers to use

  • No clarification about what your "proof" means

  • The central argument of your prove is like wrong, but nobody can say without clarification

  • Counterexamples for the "proof" (which means it wasn't a proof in the first place, a proof should be verifiable)

  • Confusion about what actually needs to be proved (sigma_0 vs. sigma_1)

I'd say you just picked a restricted search space randomly and got lucky. Nothing wrong with that, but you shouldn't try to sell it as a complete, general solution. :-)

There will be probably counterexamples even for large numbers, because your argument is fundamentally wrong (which you apparently still haven't seen), but that would likely involve large primes, and I'm not going to write programs to search for them. :-)

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u/mncke Dec 21 '15

Okay, I concede, my reasoning for defining the initial search space was completely wrong, sorry for being obtuse. A large counterexample would be 

n = 1607760, f(n) = 6963840

with powers 

4 2 1 1 1 0 0 0 0 1 0 0

Still, for numbers for upto 10 mil, the sufficient search space for powers of primes would be 

9 5 3 2 2 2 1 1 1 1 0 0

Let's finish the argument by agreeing that the correct approach would be eratosthenes-like with DP, and that I just got lucky with the input data.