Mystery of Problem 480.

General chat, humour, riddles, logic/lateral/word puzzles...
Post Reply
pismobiker
Posts: 4
Joined: Wed Nov 18, 2015 12:01 am

Mystery of Problem 480.

Post by pismobiker » Thu Aug 15, 2019 4:30 pm

I won't reveal the solution to this problem. But it is a readable word (e.g., like "tooshytokiss"). Once I solved it, I could see that one of the members (Oq0) had posed another problem: W(−P(costume)+P(eminence)−P(attained)+P(myself)−P(dissimulation)), which also produced a readable word. My question is -- how was it possible to find a collection of words that could be combined in this way to produce another word?

v6ph1
Posts: 116
Joined: Mon Aug 25, 2014 6:14 pm

Re: Mystery of Problem 480.

Post by v6ph1 » Thu Aug 15, 2019 7:35 pm

Statistics:
There are ~5*10^17 possible words in it.
And a lot of them are readable.
Now calculate all of their Numbers.
Build sums of three of them: You should find a sum which appears multiple times. (see Goldbach's conjecture)
It is guaranteed if there are at least 1.5*10^6 readable words.
And the chance for such pairs is incredibly high. (compare with birthday paradox)
You need slightly less then 9*10^8 sums to have a 50% chance for 1 hit. (if the sums are equally distributed!)
so: ~2000 words have to be readable. - I think there are more of them
Image

User avatar
yourmaths
Posts: 27
Joined: Mon Aug 25, 2014 10:00 am

Re: Mystery of Problem 480.

Post by yourmaths » Tue Aug 20, 2019 12:56 am

Problem 480 is a beautiful problem.
level = lambda number_solved: number_solved // 25
Image

Post Reply