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 double-factorial. 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
(7-1)!! - (2+0!) = 45
1*(7-0!)!! - 2 = 46
where !! is now used as the double-factorial.
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.
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Posted by Charlie
on 2017-06-24 17:32:15 |
re(2): computer results (spoilers) extended
