Let us use the first 3 digits of PI, i.e. 3,1,4 to create numbers from 1 to 50, using only basic math. operators.
Not all the digits must be used, but none can be repeated.

Examples (out of this range): 52= 13*4; 65=4^3+1; 84=14*3!

Only few numbers cannot be achieved.

Please show your list.

(In reply to re(4): hint- a DejMar I'll chip in 59 by Ady TZIDON)

I limited my solutions with (!) to subfactorials, factorials, and double factorials [and the initial given operations to the puzzle].

One can get quite far with the three numbers (there is a finite limit, though) using multifactorials in addition to the given operations. As an aid to values between 1 and 100 -- only using the number 4 with the given factorial-type functions:

 1 = !(SQRT(4))          
 2 = SQRT(4)             
 3 = SQRT((!4))          
 4 = 4              
 6 = (SQRT(!4))!       
 8 = 4!!            
 9 = !4             
16 = (4!!)!!!!!      
18 = (!4)!!!!!!       
24 =  4!            
27 = (!4)!!!!!       
32 = (4!!)!!!!           
36 = (!4)!!!!            
45 = (!4)!!!            
48 = (SQRT(!4)!)!!    
54 = (((SQRT(!4))!)!!!)!!!!!!!!!!!!!!! 
60 = ((SQRT(!4)!)!!!!)!!!!!!!
64 = ((4!!)!!!!!)!!!!!!!!!!!!
72 = (((SQRT((!4))!)!!!!)!!!!!! 
80 = (4!!)!!!
90 = (((SQRT(!4))!)!!!)!!!!!!!!!!!!!
96 = ((4!!)!!!!!)!!!!!!!!!!  

With the 1 and 3 available, with addition and subtraction (and 3!) to fill in the gaps between of following those numbers,  one see that one can reach and surpass 100 with the three digits.
    

Edited on December 30, 2015, 2:42 am

Posted by Dej Mar on 2015-12-29 06:04:59