This is a real story. A long long time ago, based on the "Four fours" problem, I wondered if I could do the same using exactly five 3īs, the restrictions a bit tighter: I could use only the 4 basic math operations, exponentiation, factorial, and all parentheses I may need. Besides, I didnīt disallow me to join two "3īs" to make "33".

Using this, and only this, I succeeded in writing expressions for all integers from 0 to 100.

To narrow your work, since a great number of integers can be easily obtained, can you find expressions for 47, 50, 56, 58, 64, 70, 71, 73, 74, 76, 77, 85, 88, 94, and 95?

(In reply to Values from one "3" by Leming)

I am surprised, from what pcbouhid implied in his comments in the queue, the factorial -- not the double factorial, multifactorial, subfactorial, superfactorial, primorial, gamma function, etc. -- was permitted. 
The only leeway I can see in the tighter restrictions given would be various types of exponentiation (such as tetration), though I have not (yet) found/sought solutions for any other than the standard exponentiation. 

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Post comment.  I see from your solutions that 3!! is meant to be (3!)!, and not the double factorial as it first appears.

Edited on July 7, 2008, 8:53 pm

Posted by Dej Mar on 2008-07-07 19:33:18