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

Home > Numbers
2017 to start with (Posted on 2017-06-23) Difficulty: 3 of 5
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.)
Solution 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/        210/7
31  ,2,0!,1+^!,7+  (2^(0!+1))!+7 <---
32  ,17,0!-,2*     (17-0!)*2
33  ,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-      7^2-10
40  
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-      60/2-1
30  ,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-        60-21
40  ,10,6,2-*      10*(6-2)
41  ,61,20-        61-20
42  ,2,0!+!,1,6+*  ((2+0!)!)*(1+6) <---
43  
44  
45  ,2,0!+!!,16/   (((2+0!)!)!)/16 <---
46  ,10,6,2^+      10+6^2
47  
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information