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Topic: Brainteaser n
Replies: 15   Last Post: Aug 6, 2003 7:10 AM

 Messages: [ Previous | Next ]
 Daniel Joseph Min Posts: 57 Registered: 12/13/04
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

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 (base-independent) shapes of naturals,
which will enhance your enjoyment and comfort in your search for beauty and
truth.

--
Bourbaki

Date Subject Author
1/13/03 Daniel Joseph Min
1/13/03 Virgil
1/13/03 Daniel Joseph Min
1/13/03 William Hart
1/13/03 William Hart
1/13/03 Daniel Joseph Min
1/13/03 William Hart
1/13/03 William Hart
1/14/03 Jeroen Boschma
1/14/03 William Hart
1/13/03 The Last Danish Pastry
1/13/03 Daniel Joseph Min
1/13/03 David C. Ullrich
1/14/03 The Last Danish Pastry
1/14/03 The Last Danish Pastry
8/6/03 anonymous