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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.

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): computer results (spoilers) extended | Comment 6 of 7 |

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.

 Posted by Charlie on 2017-06-24 17:32:15

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