
Re: Brainteaser n
Posted:
Jan 13, 2003 5:27 PM


On Mon 13 Jan 2003 05:43:16 GMT Virgil <vmhjr2@attbi.com> wrote
>(Bourbaki) wrote: snip >> 3^54 snipping low powers >>11^60 snipping low powers >>37^38 snipping low powers >> 9091^11 snip >> 9901^9 snip >> 909091^7 snip >> 99990001^4 snip >> 999999000001^3 snip >> 9999999900000001^2 snip >> 909090909090909091^2 * 1111111111111111111^5 snip >> 11111111111111111111111^4 snip >> 900900900900990990990991^2 snip >> 909090909090909090909090909091 snip >> 9090909090909090909090909090909090909090909090909091 snip >> 900900900900900900900900900900990990990990990990990990990991
snip
>> the only operators being add and multiply; no factorials
snip
>> The expression is elegant in its economy.
snip
>I reckon some kind of factorial, say of the largest prime >factor of the given number, with all the 2's and maybe some >other stuff divided out might do it.
No, no, no!
Given what is above (and I have snipped away all the subtler clues, leaving only the blatant ones), your answer is, well, quite ludicrous. :)
Correct is:
111 PI J(n):J(1)=1,J(k+1)=10*J(k)+1 n=1
or, if you prefer
REP(3) PI REP(n) n=REP(1)
Please see my reply to Bill Hart, who got half way there.
Intuition and induction are important in mathematical creativity. Virgil, I suggest you spend time pondering the (baseindependent) shapes of naturals, which will enhance your enjoyment and comfort in your search for beauty and truth.
 Bourbaki

