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?

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.

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