Using arithmetic operations, express the integers from 31 to 50.
You are allowed the standard arithmetic operations, including +, -, *, /, and square root (e.g. sqrt(4)).
The following operations may be useful :
Concatenation. 44 is valid as part of an answer.
Decimals. 4.4 is valid as part of an answer; so is .4 .
Recurring decimals. E.g. .4r (or .4recurring) is the same as .444... - or 4/9 - and valid.
Factorials. The factorial of a positive integer (written as n!) is the product of all the positive integers less than or equal to that number. E.g. 4! = 4*3*2*1 = 24.
Double factorials. The double factorial of an even positive integer (written as n!!) is the product of all the positive even integers less than or equal to that number. The double factorial of an odd positive integer is the product of all the positive odd integers less than or equal to that number. E.g. 4!! = 4 * 2 = 8, and 5!! = 5 * 3 * 1 = 15.
Powers. 4^4 means 4 to the power of 4, and 4^sqrt(4) means 4 squared (or 16). You don't actually need these for these numbers, but you can use them if you like.
Don't use operations like cube roots and inverses (e.g. 1/4). The reason for this is that in normal notation, these use numbers other than 4.
The following may also be useful :
n = sqrt(n) * sqrt(n), n being any number
0 = n-n
1 = n/n (unless n is 0)
2 = (n+n)/n
3 = (n+n+n)/n
10 = 4/.4
5 = sqrt(4)/.4
9 = 4/.4r
3 = sqrt(4/.4r)
