Mystery of Problem 480.

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 Joined: Wed Nov 18, 2015 12:01 am
Mystery of Problem 480.
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?
Re: Mystery of Problem 480.
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
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
Re: Mystery of Problem 480.
Problem 480 is a beautiful problem.
level = lambda number_solved: number_solved // 25