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

Home > Numbers
List the expressionist numbers (Posted on 2016-05-30) Difficulty: 4 of 5
Consider numbers like 343 or 2592.
343=(3+4)^3
2592=2^5*9^2.

We have just shown that some numbers stay unchanged when a number of mathematical operators are added /inserted, without changing the order of the digits.
Within our puzzle lets call those numbers expressionist numbers.
Let us limit the set of acceptable mathematical symbols to the following operators: +, -, *, /, ^, sqrt, !. and any amount of brackets.

My questions:
In the period between 10 A.D. & 2016 A.D. what years were labeled by expressionist numbers?
How many such years will there be between 2017 A.D. & 9999 A.D.?

Bonus: How about one, two (or more) 5-digit examples?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Supplement to part 1 list | Comment 7 of 10 |
This list below contains some repeat numbers from the original list, but also some new numbers, enabled by allowing a unary negative sign at the beginning:

24    -24r^!                  -2^sqrt(4)!
120   -120!+!+!               (-1+(2+0!)!)!
127   -127^+                  -1+2^7
143   -14!3!*+                -1+4!*3!
144   -14+!4!*                (-1+4)!*4!
324   -32r*4^                 (-3*sqrt(2))^4
343   -34-3!^r                sqrt((-3-4)^3!)
595   -59r!!+5!-              -5+sqrt(9)!!-5!
713   -71*3!!+                -7*1+3!!
720   -72^r0!-!               (sqrt(-7^2)-0!)!
729   -72-9r!^r               sqrt((-7-2)^sqrt(9)!)
1294  -12*9r!4^+              -1*2+sqrt(9)!^4
1432  -14*3!!+2*              (-1*4+3!!)*2
1433  -14r3!!*+3!-            -1+sqrt(4)*3!!-3!
1434  -14r-3!!+4r*            (-1-sqrt(4)+3!!)*sqrt(4)
1435  -14+!!3!!+5-            (-1+4)!!+3!!-5
1436  -14*3!!+6!+             -1*4+3!!+6!
1439  -14r3!!r*9r!!r*+        -1+sqrt(4)*sqrt(3!!)*sqrt(sqrt(9)!!)
1440  -14+!!4r*               (-1+4)!!*sqrt(4)
1441  -14+!!4r*1+             (-1+4)!!*sqrt(4)+1
1442  -14+!!4r*2+             (-1+4)!!*sqrt(4)+2
1443  -14r4r3!!+*+            -1+sqrt(4)*(sqrt(4)+3!!)
1444  -14+!!4r+4r*            ((-1+4)!!+sqrt(4))*sqrt(4)
1445  -14+!!4r*5+             (-1+4)!!*sqrt(4)+5
1446  -14+!!4r*6+             (-1+4)!!*sqrt(4)+6
1447  -14+!!4r*7+             (-1+4)!!*sqrt(4)+7
1448  -14+!!4r*8+             (-1+4)!!*sqrt(4)+8
1449  -14r-4!^rr9r!!+         sqrt(sqrt((-1-sqrt(4))^4!))+sqrt(9)!!
1463  -14!+6!+3!!+            -1+4!+6!+3!!
1464  -14+!!6!+4!+            (-1+4)!!+6!+4!
1673  -16-7!3/+               -1-6+7!/3
1679  -16!7*9r/+              -1+6!*7/sqrt(9)
1764  -17r*6r*4^              (-1*sqrt(7)*sqrt(6))^4
1944  -19r!rr*4!^4!/          (-1*sqrt(sqrt(sqrt(9)!)))^4!/4!

  Posted by Charlie on 2016-05-31 08:40:44
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 (3)
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