All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

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.)
 computer results (spoilers) | Comment 3 of 7 |
The table below shows formulae for up to 50.

Of the first 40 that are asked for, of these, 30, marked with  <---, were able to be represented with the digits in the correct order: 2017.  Eight were found only with permuted digits and two were not found at all (38 and 40).

`1  ,2,0,17^^       2^0^17 <---2  ,2,0,17^+       2+0^17 <---3  ,20,17-         20-17 <---4  ,2,0!,1,7^+^    2^(0!+1^7) <---5  ,2,0,1-/,7+     2/(0-1)+7 <---6  ,20,17-!        (20-17)! <---7  ,2,0,1^^,7*     2^0^1*7 <---8  ,2,0,1,7-+-     2-(0+1-7) <---9  ,2,0,1,7*++     2+0+1*7 <---10  ,2,0,1,7+++    2+0+1+7 <---11  ,2,0!,1,7+++   2+0!+1+7 <---12  ,20,1,7+-      20-(1+7) <---13  ,20,1,7*-      20-1*7 <---14  ,20,1,7-+      20+1-7 <---15  ,17,2,0+-      17-(2+0)16  ,2,0,1,7++*    2*(0+1+7) <---17  ,2,0^,17*      2^0*17 <---18  ,2,0^,17+      2^0+17 <---19  ,20,1,7^-      20-1^7 <---20  ,20,1,7^^      20^1^7 <---21  ,20,1,7^+      20+1^7 <---22  ,1,7,2,0!+*+   1+7*(2+0!)23  ,2,0!+!,17+    (2+0!)!+17 <---24  ,2,0!,1,7^+^!  (2^(0!+1^7))! <---25  ,1,7,2,0!+-!+  1+(7-(2+0!))!26  ,20,1,7--      20-(1-7) <---27  ,20,1,7*+      20+1*7 <---28  ,20,1,7++      20+1+7 <---29  ,1,27,0!++     1+27+0!30  ,210,7/        210/731  ,2,0!,1+^!,7+  (2^(0!+1))!+7 <---32  ,17,0!-,2*     (17-0!)*233  ,17,2*,0!-     17*2-0!34  ,2,0,17+*      2*(0+17) <---35  ,2,0!+!,1-,7*  (((2+0!)!)-1)*7 <---36  ,2,0!,17+*     2*(0!+17) <---37  ,20,17+        20+17 <---38  39  ,7,2^,10-      7^2-1040  41  ,1,2+!,7*,0!-  (((1+2)!)*7)-0!42  ,2,0,1^!+!,7*  ((2+(0^1)!)!)*7 <---43  ,1,7,2,0!+!*+  1+7*((2+0!)!)44  45  46  47  ,7,2^,1,0!+-   7^2-(1+0!)48  ,2,0!+!,1,7+*  ((2+0!)!)*(1+7) <---49  ,2,0!+!,1+,7*  ((2+0!)!+1)*7 <---50  ,1,7,2,0+^+    1+7^(2+0)`

on the other hand, working with 2016 gives a full set of solutions for the first 40 integers:

`1  ,2,0,16^^       2^0^16 <---2  ,2,0,16^+       2+0^16 <---3  ,2,0,16^!+      2+(0^16)! <---4  ,20,16-         20-16 <---5  ,2,0*,1,6--     2*0-(1-6) <---6  ,2,0,16^!+!     (2+(0^16)!)! <---7  ,2,0,1,6-+-     2-(0+1-6) <---8  ,2,0,1,6*++     2+0+1*6 <---9  ,2,0,1,6+++     2+0+1+6 <---10  ,2,0,1,6--*    2*(0-(1-6)) <---11  ,2,0!+!,1,6--  ((2+0!)!)-(1-6) <---12  ,2,0,1,6/+/    2/(0+1/6) <---13  ,20,1,6+-      20-(1+6) <---14  ,20,1,6*-      20-1*6 <---15  ,20,1,6-+      20+1-6 <---16  ,2,0^,16*      2^0*16 <---17  ,2,0^,16+      2^0+16 <---18  ,2,0,16++      2+0+16 <---19  ,20,1,6^-      20-1^6 <---20  ,20,1,6^^      20^1^6 <---21  ,20,1,6^+      20+1^6 <---22  ,2,0!+!,16+    (2+0!)!+16 <---23  ,1,6,2/+!,0!-  ((1+6/2)!)-0!24  ,20,16-!       (20-16)! <---25  ,20,1,6--      20-(1-6) <---26  ,20,1,6*+      20+1*6 <---27  ,20,1,6++      20+1+6 <---28  ,1,26,0!++     1+26+0!29  ,60,2/,1-      60/2-130  ,2,0!,1+^!,6+  (2^(0!+1))!+6 <---31  ,16,2*,0!-     16*2-0!32  ,2,0,16+*      2*(0+16) <---33  ,16,2*,0!+     16*2+0!34  ,2,0!,16+*     2*(0!+16) <---35  ,1,6,2^,0!-*   1*(6^2-0!)36  ,20,16+        20+16 <---37  ,1,6,2,0+^+    1+6^(2+0)38  ,1,6,2^,0!++   1+6^2+0!39  ,60,21-        60-2140  ,10,6,2-*      10*(6-2)41  ,61,20-        61-2042  ,2,0!+!,1,6+*  ((2+0!)!)*(1+6) <---43  44  45  ,2,0!+!!,16/   (((2+0!)!)!)/16 <---46  ,10,6,2^+      10+6^247  48  ,2,0!+,16*     (2+0!)*16 <---49  ,1,6+,2,0+^    (1+6)^(2+0)50  ,1,6+,2^,0!+   (1+6)^2+0!`

 Posted by Charlie on 2017-06-23 18:11:50

 Search: Search body:
Forums (1)