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!
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Posted by Charlie
on 2017-06-23 18:11:50 |
computer results (spoilers)
