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 The five 3īs (Posted on 2008-07-07)
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?

 Submitted by pcbouhid Rating: 4.5000 (2 votes) Solution: (Hide) See the various solutions in the comments.

 Subject Author Date Four Fours brianjn 2008-07-12 23:12:12 re(5): all hundred Charlie 2008-07-09 11:45:00 re(6): all hundred Charlie 2008-07-09 11:40:10 re(5): all hundred Charlie 2008-07-09 11:39:07 re(4): all hundred Charlie 2008-07-09 11:37:35 re(3): all hundred Leming 2008-07-09 09:53:15 re(2): all hundred Dej Mar 2008-07-08 22:49:43 re: all hundred Dej Mar 2008-07-08 20:02:56 re: all hundred Leming 2008-07-08 17:32:22 all hundred Charlie 2008-07-08 14:14:34 the shortest representation of each Charlie 2008-07-08 12:15:01 re(5): all the asked-for numbers (spoilers) Charlie 2008-07-08 11:48:29 re(4): all the asked-for numbers (spoilers) Charlie 2008-07-08 11:47:42 re(3): all the asked-for numbers (spoilers) Charlie 2008-07-08 11:46:47 re(2): all the asked-for numbers (spoilers) Charlie 2008-07-08 11:45:10 re: all the asked-for numbers (spoilers) Charlie 2008-07-08 11:43:59 all the asked-for numbers (spoilers) Charlie 2008-07-08 11:41:52 re: my short answer pcbouhid 2008-07-08 07:59:26 my short answer Ady TZIDON 2008-07-07 23:27:01 re(2): Values from one pcbouhid 2008-07-07 22:53:44 re: Values from one Dej Mar 2008-07-07 20:21:06 Partial solution (spoiler) Dej Mar 2008-07-07 19:47:45 re: Values from one Dej Mar 2008-07-07 19:33:18 re: Solution using five 3's pcbouhid 2008-07-07 19:18:03 Solution using five 3's Leming 2008-07-07 18:19:53 re: First of the list ---------- no pcbouhid 2008-07-07 16:34:55 still not all, even with exponentiation (spoilers present) Charlie 2008-07-07 15:51:13 still not all, even with exponentiation (spoilers present) Charlie 2008-07-07 15:51:06 geeky computer solution for some values (spoilers present) Charlie 2008-07-07 14:47:24 Some thoughts. Leming 2008-07-07 14:33:44 First of the list Leming 2008-07-07 14:19:16 re(2): Values from two - one more Leming 2008-07-07 14:16:49 re: Values from two - one more pcbouhid 2008-07-07 14:06:41 Values from two "3"s Leming 2008-07-07 12:54:01 Values from one "3" Leming 2008-07-07 11:59:47

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