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### Mystery of Problem 480.

Posted: **Thu Aug 15, 2019 5:30 pm**

by **pismobiker**

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.

Posted: **Thu Aug 15, 2019 8:35 pm**

by **v6ph1**

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

### Re: Mystery of Problem 480.

Posted: **Tue Aug 20, 2019 1:56 am**

by **yourmaths**

Problem 480 is a beautiful problem.