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(2): hint- not a spoiler yet by Ady TZIDON)

First,
by permitting the double factorial
46 = (3!)!! - SQRT(4) and
50 = (3!)!! + SQRT(4).

51 = (3!)!! + 4 - 1
52 = (3!)!! + 4
53 = (3!)!! + 4 + 1
54 = (3!)!! + (4 - 1)!
55 = (3!)!! + 4!! - 1 -- or 4! + 31
56 = (3!)!! + 4!!
57 = (3!)!! + 4!! + 1 -- or, as subfactorials are permitted --
        (3!)!! + !4
58 = (3!)!! + !4 + 1

A solution exists for 60 to 65, but one was not found for 59, which may not have a solution with the given operators. Thus 58 may be as high as one can go. {Primes are difficult the higher one goes.}

Edited on December 29, 2015, 3:01 am

Posted by Dej Mar on 2015-12-28 10:17:07