1. A puzzle book challenged its readers to form an expression using five threes and basic mathematical symbols to come up with 37.
   The answer was found simply enough:
   
   33 + 3 + 3/3 = 37.
   
   Find another way to do this.
   
   
2. The same puzzle book posed the problem of finding 55 using five fours and any mathematical symbols.
   That is also easily accomplished by:
   
   44 + 44/4 = 55.
   
   Find another way to do this one, as well.

Though restricted from the solution for (1), the following athematical symbols are indicated as usable for the solution for (2) as the problem states that any mathematical symbols are permitted.

SQRT(x) = square root function [substituted for radical symbol]

.x = repeating decimal

!x = subfactorial of x

x$ = superfactorial of x (as defined by Sloane and Plouffe)

|_ x _| = floor function of x

Six of several possible solutions for (1) Five 3s:
1] 333/3/3
2] 333/(3*3)
3] 3! * 3! + (3/3)³
4] 33 + (3! + 3!)/3
5] 33 + 3! - 3!/3
6] (3*3*3) + (3/.3)

Twelve of several possible solutions for (2) Five 4s:
1] (4! + 4)*SQRT(4) - 4/4
2] (4! - ((4 + 4)/4))/.4
3] 4/4 * (4! - SQRT(4))/.4
4] |_ 444/4/SQRT(4) _|
5] |_ (!(4 + SQRT(4)) - 44)/4 _|
6] 4$ * 4 + !4 - 4/SQRT(4)
7] 44/.4/4/SQRT(4)
8] 4!*SQRT(4) + SQRT(4) + SQRT(4)/.4
9] 4! + 4! + SQRT(4) + SQRT(4)/.4
10] 44 + !4 + 4/SQRT(4)
11] 4*4*4 - 4/.4
12] 4^{(4 - 4/4)} - !4

Edited on May 11, 2006, 6:28 am

Posted by Dej Mar on 2006-05-11 06:06:25