All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
The five 3īs (Posted on 2008-07-07) Difficulty: 2 of 5
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?

See The Solution Submitted by pcbouhid    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re(3): all the asked-for numbers (spoilers) | Comment 22 of 35 |
(In reply to re(2): all the asked-for numbers (spoilers) by Charlie)

3,3!,3!/,3!!^+,3^            (3+(3!/3!)^3!!)^3              64 
3,3!,3!/,3!!^-,3!^           (3-(3!/3!)^3!!)^3!             64
3,3!,3!/,3!^+,3^             (3+(3!/3!)^3!)^3               64
3,3!,3!/,3!^-,3!^            (3-(3!/3!)^3!)^3!              64
3,3!,3!/,3^+,3^              (3+(3!/3!)^3)^3                64
3,3!,3!/,3^-,3!^             (3-(3!/3!)^3)^3!               64
3,3!,3!/-,3!,3-!^            (3-3!/3!)^(3!-3)!              64
3,3!,3!/-,3,3+^              (3-3!/3!)^(3+3)                64
3,3!,3!//!,3/,3!^            ((3/(3!/3!))!/3)^3!            64
3,3!,3!/^!,3/,3!^            (3^(3!/3!)!/3)^3!              64
3,3!,3++,3!/,3!^             ((3+3!+3)/3!)^3!               64
3,3!,3++,3/,3^               ((3+3!+3)/3)^3                 64
3,3!,3+,3!//,3!^             (3/((3!+3)/3!))^3!             64
3,3!,3+/,3!*,3!^             ((3/(3!+3))*3!)^3!             64
3,3!,3,3!!-^!+,3^            (3+3!^(3-3!!)!)^3              64
3,3!,3,3!!-^!-,3!^           (3-3!^(3-3!!)!)^3!             64
3,3!,3,3!+/*!,3!^            (3*3!/(3+3!))!^3!              64
3,3!,3,3*/*!,3!^             (3*3!/(3*3))!^3!               64
3,3!,3,3+-!+,3^              (3+(3!-(3+3))!)^3              64
3,3!,3,3+-!-,3!^             (3-(3!-(3+3))!)^3!             64
3,3!,3,3+/+,3^               (3+3!/(3+3))^3                 64
3,3!,3,3+/-,3!^              (3-3!/(3+3))^3!                64
3,3!,3,3-*!+,3^              (3+(3!*(3-3))!)^3              64
3,3!,3,3-*!-,3!^             (3-(3!*(3-3))!)^3!             64
3,3!,3,3-^+,3^               (3+3!^(3-3))^3                 64
3,3!,3,3-^-,3!^              (3-3!^(3-3))^3!                64
3,3!,3-!!,3!!-!+,3^          (3+((3!-3)!!-3!!)!)^3          64
3,3!,3-!!,3!!-!-,3!^         (3-((3!-3)!!-3!!)!)^3!         64
3,3!,3-!!,3!!/+,3^           (3+(3!-3)!!/3!!)^3             64
3,3!,3-!!,3!!/-,3!^          (3-(3!-3)!!/3!!)^3!            64
3,3!,3-!,3!-!+,3^            (3+((3!-3)!-3!)!)^3            64
3,3!,3-!,3!-!-,3!^           (3-((3!-3)!-3!)!)^3!           64
3,3!,3-!,3!/+,3^             (3+(3!-3)!/3!)^3               64
3,3!,3-!,3!/-,3!^            (3-(3!-3)!/3!)^3!              64
3,3!,3-+,3/,3!^              ((3+3!-3)/3)^3!                64
3,3!,3-,3-!+,3^              (3+(3!-3-3)!)^3                64
3,3!,3-,3-!-,3!^             (3-(3!-3-3)!)^3!               64
3,3!,3-,3/+,3^               (3+(3!-3)/3)^3                 64
3,3!,3-,3/-,3!^              (3-(3!-3)/3)^3!                64
3,3!,3--!,3+,3^              ((3-(3!-3))!+3)^3              64
3,3!,3-/,3+,3^               (3/(3!-3)+3)^3                 64
3,3!,3/*,3/,3!^              ((3*3!/3)/3)^3!                64
3,3!,3/+,3-,3!^              (3+3!/3-3)^3!                  64
3,3!,3/,3!^*,3/              3*(3!/3)^3!/3                  64
3,3!,3/,3!^+,3-              3+(3!/3)^3!-3                  64
3,3!,3/,3!^,3-+              3+(3!/3)^3!-3                  64
3,3!,3/,3!^,3/*              3*(3!/3)^3!/3                  64
3,3!,3/,3-+,3!^              (3+3!/3-3)^3!                  64
3,3!,3/,3--,3^               (3-(3!/3-3))^3                 64
3,3!,3/,3/*!,3!^             (3*(3!/3)/3)!^3!               64
3,3!,3/-,3+,3^               (3-3!/3+3)^3                   64
3,3!-,3!+!,3/,3!^            ((3-3!+3!)!/3)^3!              64
3,3!-,3+!,3+,3^              ((3-3!+3)!+3)^3                64
3,3!-,3/,3+,3!^              ((3-3!)/3+3)^3!                64
3,3!/,3!!,3!!,3!+-^          (3/3!)^(3!!-(3!!+3!))          64
3,3!/,3!!,3!!-,3!-^          (3/3!)^(3!!-3!!-3!)            64
3,3!/,3!!,3!,3!!+-^          (3/3!)^(3!!-(3!+3!!))          64
3,3!/,3!!,3!-,3!!-^          (3/3!)^(3!!-3!-3!!)            64
3,3!/,3!*!,3/,3!^            (((3/3!)*3!)!/3)^3!            64
3,3!/,3!,3!,3!+-^            (3/3!)^(3!-(3!+3!))            64
3,3!/,3!,3!-,3!-^            (3/3!)^(3!-3!-3!)              64
3,3!/,3,3!,3+-^              (3/3!)^(3-(3!+3))              64
3,3!/,3,3!-,3-^              (3/3!)^(3-3!-3)                64
3,3!/,3,3,3!+-^              (3/3!)^(3-(3+3!))              64
3,3!/,3,3,3*-^               (3/3!)^(3-3*3)                 64
3,3!/,3,3-,3!-^              (3/3!)^(3-3-3!)                64
3,3*,3!-!,3/,3!^             ((3*3-3!)!/3)^3!               64
3,3*,3+,3!/,3!^              ((3*3+3)/3!)^3!                64
3,3*,3+,3/,3^                ((3*3+3)/3)^3                  64
3,3*,3-,3/,3!^               ((3*3-3)/3)^3!                 64
3,3*,3/!,3/,3!^              ((3*3/3)!/3)^3!                64
3,3+!,3!!+,3!!/,3!^          (((3+3)!+3!!)/3!!)^3!          64
3,3+!,3!!-!,3+,3^            (((3+3)!-3!!)!+3)^3            64
3,3+!,3!!/,3+,3^             ((3+3)!/3!!+3)^3               64
3,3+,3!+,3!/,3!^             ((3+3+3!)/3!)^3!               64
3,3+,3!+,3/,3^               ((3+3+3!)/3)^3                 64
3,3+,3!,3-/,3!^              ((3+3)/(3!-3))^3!              64
3,3+,3!,3/-,3^               (3+3-3!/3)^3                   64
3,3+,3!-!,3+,3^              ((3+3-3!)!+3)^3                64
3,3+,3!/,3+,3^               ((3+3)/3!+3)^3                 64
3,3+,3!^,3,3!^/              (3+3)^3!/3^3!                  64
3,3+,3-!,3/,3!^              ((3+3-3)!/3)^3!                64
3,3+,3/,3!,3-!^              ((3+3)/3)^(3!-3)!              64
3,3+,3/,3,3+^                ((3+3)/3)^(3+3)                64
3,3,3!!,3!!-*!+,3^           (3+(3*(3!!-3!!))!)^3           64
3,3,3!!,3!!-*!-,3!^          (3-(3*(3!!-3!!))!)^3!          64
3,3,3!!,3!!-^+,3^            (3+3^(3!!-3!!))^3              64
3,3,3!!,3!!-^-,3!^           (3-3^(3!!-3!!))^3!             64
3,3,3!!-^!,3+,3^             (3^(3-3!!)!+3)^3               64
3,3,3!!/,3!!^!+,3^           (3+(3/3!!)^3!!!)^3             64
3,3,3!!/,3!!^!-,3!^          (3-(3/3!!)^3!!!)^3!            64
3,3,3!++,3!/,3!^             ((3+3+3!)/3!)^3!               64
3,3,3!++,3/,3^               ((3+3+3!)/3)^3                 64
3,3,3!+,3!//,3!^             (3/((3+3!)/3!))^3!             64
3,3,3!+/,3!*,3!^             ((3/(3+3!))*3!)^3!             64
3,3,3!,3!!-^!+,3^            (3+3^(3!-3!!)!)^3              64
3,3,3!,3!!-^!-,3!^           (3-3^(3!-3!!)!)^3!             64
3,3,3!,3!-*!+,3^             (3+(3*(3!-3!))!)^3             64
3,3,3!,3!-*!-,3!^            (3-(3*(3!-3!))!)^3!            64
3,3,3!,3!-^+,3^              (3+3^(3!-3!))^3                64
3,3,3!,3!-^-,3!^             (3-3^(3!-3!))^3!               64
3,3,3!,3--!+,3^              (3+(3-(3!-3))!)^3              64
3,3,3!,3--!-,3!^             (3-(3-(3!-3))!)^3!             64
3,3,3!,3-/+,3^               (3+3/(3!-3))^3                 64
3,3,3!,3-/-,3!^              (3-3/(3!-3))^3!                64
3,3,3!,3/,3!^--              3-(3-(3!/3)^3!)                64
3,3,3!,3/,3!^//              3/(3/(3!/3)^3!)                64
3,3,3!,3/-+,3^               (3+3-3!/3)^3                   64
3,3,3!,3/--,3!^              (3-(3-3!/3))^3!                64
3,3,3!,3///,3!^              (3/(3/(3!/3)))^3!              64
3,3,3!-+!,3+,3^              ((3+3-3!)!+3)^3                64
3,3,3!-,3+!+,3^              (3+(3-3!+3)!)^3                64
3,3,3!-,3+!-,3!^             (3-(3-3!+3)!)^3!               64
3,3,3!-,3/+,3!^              (3+(3-3!)/3)^3!                64
3,3,3!-,3/-,3^               (3-(3-3!)/3)^3                 64
3,3,3!--,3/,3!^              ((3-(3-3!))/3)^3!              64
3,3,3!-/,3+,3!^              (3/(3-3!)+3)^3!                64
3,3,3!/,3!^,3*/              3/((3/3!)^3!*3)                64
3,3,3!/,3!^/,3/              (3/(3/3!)^3!)/3                64
3,3,3!/,3*/,3!^              (3/((3/3!)*3))^3!              64
3,3,3!//,3/,3!^              ((3/(3/3!))/3)^3!              64
3,3,3*+,3!/,3!^              ((3+3*3)/3!)^3!                64
3,3,3*+,3/,3^                ((3+3*3)/3)^3                  64
3,3,3*,3!//,3!^              (3/(3*3/3!))^3!                64
3,3,3*/,3!*,3!^              ((3/(3*3))*3!)^3!              64
3,3,3+!,3!!-!+,3^            (3+((3+3)!-3!!)!)^3            64
3,3,3+!,3!!-!-,3!^           (3-((3+3)!-3!!)!)^3!           64
3,3,3+!,3!!/+,3^             (3+(3+3)!/3!!)^3               64
3,3,3+!,3!!/-,3!^            (3-(3+3)!/3!!)^3!              64
3,3,3+,3!-!+,3^              (3+(3+3-3!)!)^3                64
3,3,3+,3!-!-,3!^             (3-(3+3-3!)!)^3!               64
3,3,3+,3!/+,3^               (3+(3+3)/3!)^3                 64
3,3,3+,3!/-,3!^              (3-(3+3)/3!)^3!                64
3,3,3,3!!-^!+,3^             (3+3^(3-3!!)!)^3               64
3,3,3,3!!-^!-,3!^            (3-3^(3-3!!)!)^3!              64
3,3,3,3!-+!+,3^              (3+(3+3-3!)!)^3                64
3,3,3,3!-+!-,3!^             (3-(3+3-3!)!)^3!               64
3,3,3,3!-/+,3!^              (3+3/(3-3!))^3!                64
3,3,3,3!-/-,3^               (3-3/(3-3!))^3                 64
3,3,3,3!/*/,3!^              (3/(3*3/3!))^3!                64
3,3,3,3!/,3!^*/              3/(3*(3/3!)^3!)                64
3,3,3,3-*!+,3^               (3+(3*(3-3))!)^3               64
3,3,3,3-*!-,3!^              (3-(3*(3-3))!)^3!              64
3,3,3,3-^+,3^                (3+3^(3-3))^3                  64
3,3,3,3-^-,3!^               (3-3^(3-3))^3!                 64
3,3,3-!*!,3/,3!^             ((3*(3-3)!)!/3)^3!             64
3,3,3-!+!,3!/,3^             ((3+(3-3)!)!/3!)^3             64
3,3,3-!+,3!,3-^              (3+(3-3)!)^(3!-3)              64
3,3,3-!,3!!^+,3^             (3+(3-3)!^3!!)^3               64
3,3,3-!,3!!^-,3!^            (3-(3-3)!^3!!)^3!              64
3,3,3-!,3!^+,3^              (3+(3-3)!^3!)^3                64
3,3,3-!,3!^-,3!^             (3-(3-3)!^3!)^3!               64
3,3,3-!,3^+,3^               (3+(3-3)!^3)^3                 64
3,3,3-!,3^-,3!^              (3-(3-3)!^3)^3!                64
3,3,3-!-,3!,3-!^             (3-(3-3)!)^(3!-3)!             64
3,3,3-!-,3,3+^               (3-(3-3)!)^(3+3)               64
3,3,3-!/!,3/,3!^             ((3/(3-3)!)!/3)^3!             64
3,3,3-!^!,3/,3!^             (3^(3-3)!!/3)^3!               64
3,3,3-*!,3+,3^               ((3*(3-3))!+3)^3               64
3,3,3-+!,3/,3!^              ((3+3-3)!/3)^3!                64
3,3,3-,3!!*!+,3^             (3+((3-3)*3!!)!)^3             64
3,3,3-,3!!*!-,3!^            (3-((3-3)*3!!)!)^3!            64
3,3,3-,3!!/!+,3^             (3+((3-3)/3!!)!)^3             64
3,3,3-,3!!/!-,3!^            (3-((3-3)/3!!)!)^3!            64
3,3,3-,3!*!+,3^              (3+((3-3)*3!)!)^3              64
3,3,3-,3!*!-,3!^             (3-((3-3)*3!)!)^3!             64
3,3,3-,3!/!+,3^              (3+((3-3)/3!)!)^3              64
3,3,3-,3!/!-,3!^             (3-((3-3)/3!)!)^3!             64
3,3,3-,3*!+,3^               (3+((3-3)*3)!)^3               64
3,3,3-,3*!-,3!^              (3-((3-3)*3)!)^3!              64
3,3,3-,3/!+,3^               (3+((3-3)/3)!)^3               64
3,3,3-,3/!-,3!^              (3-((3-3)/3)!)^3!              64
3,3,3--!,3/,3!^              ((3-(3-3))!/3)^3!              64
3,3,3-^,3+,3^                (3^(3-3)+3)^3                  64
3,3,3/*!,3/,3!^              ((3*3/3)!/3)^3!                64
3,3,3/+!,3!/,3^              ((3+3/3)!/3!)^3                64
3,3,3/+,3!,3-^               (3+3/3)^(3!-3)                 64
3,3,3/,3!!^+,3^              (3+(3/3)^3!!)^3                64
3,3,3/,3!!^-,3!^             (3-(3/3)^3!!)^3!               64
3,3,3/,3!^+,3^               (3+(3/3)^3!)^3                 64
3,3,3/,3!^-,3!^              (3-(3/3)^3!)^3!                64
3,3,3/,3^+,3^                (3+(3/3)^3)^3                  64
3,3,3/,3^-,3!^               (3-(3/3)^3)^3!                 64
3,3,3/-,3!,3-!^              (3-3/3)^(3!-3)!                64
3,3,3/-,3,3+^                (3-3/3)^(3+3)                  64
3,3,3//!,3/,3!^              ((3/(3/3))!/3)^3!              64
3,3,3/^!,3/,3!^              (3^(3/3)!/3)^3!                64
3,3-!,3!!,3!!-!+,3!^         ((3-3)!+(3!!-3!!)!)^3!         64
3,3-!,3!!,3!!/+,3!^          ((3-3)!+3!!/3!!)^3!            64
3,3-!,3!!^,3+,3^             ((3-3)!^3!!+3)^3               64
3,3-!,3!*,3/,3!^             ((3-3)!*3!/3)^3!               64
3,3-!,3!+,3-,3^              ((3-3)!+3!-3)^3                64
3,3-!,3!,3!-!+,3!^           ((3-3)!+(3!-3!)!)^3!           64
3,3-!,3!,3!/+,3!^            ((3-3)!+3!/3!)^3!              64
3,3-!,3!,3-+,3^              ((3-3)!+3!-3)^3                64
3,3-!,3!,3/*,3!^             ((3-3)!*3!/3)^3!               64
3,3-!,3!,3/,3!^*             (3-3)!*(3!/3)^3!               64
3,3-!,3!^,3+,3^              ((3-3)!^3!+3)^3                64
3,3-!,3*!,3/,3!^             (((3-3)!*3)!/3)^3!             64
3,3-!,3+!,3!/,3^             (((3-3)!+3)!/3!)^3             64
3,3-!,3+,3!,3-^              ((3-3)!+3)^(3!-3)              64
3,3-!,3,3!--,3^              ((3-3)!-(3-3!))^3              64
3,3-!,3,3!/,3!^/             (3-3)!/(3/3!)^3!               64
3,3-!,3,3!//,3!^             ((3-3)!/(3/3!))^3!             64
3,3-!,3,3-!+,3!^             ((3-3)!+(3-3)!)^3!             64

  Posted by Charlie on 2008-07-08 11:46:47
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information