How many integers from 1 to 40 can you form using all 4 digits 2, 0, 1, and 7 exactly once each; the operators
+, –, ×, /, ^, concatenation and ! ?
Any number of parenthesis may be used.
Examples:
1=217^0;
2=2+0*17;
3=21/7+0
...
etc
Team work (adding so far unresolved numbers ) encouraged.
(In reply to
re: computer results (spoilers) extended by Ady TZIDON)
Well, for 40, 45 and 46, for 2017 I can get
40 ,2,0!+!:,1,7+
...
45 ,7,1:,2,0!+
46 ,1,7,0!*:,2
where : represents doublefactorial. I'm using : to represent it so as not to confuse with the factorial of a factorial
They translate to
((2+0!)!)!!(1+7) = 40
(71)!!  (2+0!) = 45
1*(70!)!!  2 = 46
where !! is now used as the doublefactorial.
While 35 = 7*10/2 is a neater formula than (((2+0!)!)1)*7, I gave precedence to formulae having the digits in order, regardless of niceness of the formula.

Posted by Charlie
on 20170624 17:32:15 