This is a python3 program that can solve the 24 game by enumerating all possible expressions. It also supports advanced rules(e.g.exponentiation and logarithm).
Allow advanced operators?
Advanced operators disabled
Allow unary operator?
Unary operator disabled
Enumerate all target?
Just solve one target
Enter a target:
Target is 24
--------------------
Enter some numbers:4 6 8 10
24 = 4-10*(6-8)
24 = 10*(8-6)+4
24 = 8-4*(6-10)
24 = (10-6)*4+8
4 solution(s) in 0.266 seconds
28 duplication(s)
31104 combination(s)
--------------------
Enter some numbers:6 6 7 8
0 solution(s) in 0.266 seconds
0 duplication(s)
28800 combination(s)
--------------------
Enter some numbers:4 4 10 10
24 = (10*10-4)/4
1 solution(s) in 0.229 seconds
15 duplication(s)
26496 combination(s)
--------------------
Enter some numbers:3 3 8 8
24 = 8/(3-8/3)
1 solution(s) in 0.234 seconds
31 duplication(s)
26496 combination(s)
--------------------
Allow advanced operators?
Advanced operators disabled
Allow unary operator?
Unary operator disabled
Enumerate all target?
Just solve one target
Enter a target:36
Target is 36
--------------------
Enter some numbers:4 9 8 4
36 = 8*(9-4)-4
1 solution(s) in 0.252 seconds
15 duplication(s)
28800 combination(s)
--------------------
Enter some numbers:4 1 7 3
36 = (1+4+7)*3
36 = (1+7+4)*3
36 = (3-(1-7))*4
36 = (3+7-1)*4
36 = 4*(7-(1-3))
36 = (3-1+7)*4
6 solution(s) in 0.270 seconds
58 duplication(s)
31104 combination(s)
Exponentiation, logarithm, permutation number and combination number are supported.
Allow advanced operators?y
Advanced operators enabled
Allow unary operator?
Unary operator disabled
Enumerate all target?
Just solve one target
Enter a target:
Target is 24
--------------------
Enter some numbers:2 3 10 10
24 = 2/10*C(10, 3)
24 = C(10, 3)/(10/2)
24 = 2^10-10^3
24 = 10-2*(3-10)
24 = (10-3)*2+10
24 = 2*C(10, 3)/10
24 = 2/(10/C(10, 3))
7 solution(s) in 3.184 seconds
169 duplication(s)
357504 combination(s)
--------------------
Enter some numbers:2 2 2 6
24 = P(6-2, 2/2)
24 = P(6-2, log_2(2))
24 = P(6-2, C(2, 2))
24 = P(6-2, P(2, 2))
24 = 2*P(6-2, 2)
24 = 2^(2+log_2(6))
6 solution(s) in 2.461 seconds
282 duplication(s)
282240 combination(s)
--------------------
Enter some numbers:6 7 9 10
24 = 10*6-C(9, 7)
24 = 6^(10-7)/9
2 solution(s) in 3.517 seconds
22 duplication(s)
395136 combination(s)
--------------------
Currently, squreroot and factorial are supported.
Allow advanced operators?y
Advanced operators enabled
Allow unary operator?y
Unary operator enabled
Number of unary operators allowed:
1 unary operators allowed
Enumerate all target?
Just solve one target
Enter a target:
Target is 24
--------------------
Enter some numbers:1 1 1 1
24 = (1+1+1+1)!
24 = ((1+1)*(1+1))!
24 = ((1+1)^(1+1))!
3 solution(s) in 7.457 seconds
237 duplication(s)
690336 combination(s)
--------------------
Enter some numbers:15 9 9 2
24 = (15+9)*(sqrt(9)-2)
24 = (15+9)/(sqrt(9)-2)
24 = 15-9+2*9
24 = (15-9+2)*sqrt(9)
24 = sqrt(2^(15-9)*9)
24 = ((15-9)^2/9)!
24 = 9+C(15-9, 2)
24 = 2*9-(9-15)
24 = (2-(9-15))*sqrt(9)
24 = sqrt(9/2^(9-15))
24 = ((9-15)^2/9)!
24 = 2*sqrt(15*9+9)
24 = (15+2-9)*sqrt(9)
24 = sqrt(9)-(9-15*2)
24 = 15*2-9+sqrt(9)
24 = 15*2-(9-sqrt(9))
24 = 15*2+sqrt(9)-9
24 = (15^2-9)/9
24 = (9+9)/2+15
24 = (log_2(15+9/9))!
24 = (log_2(15+log_9(9)))!
24 = (log_2(15+C(9, 9)))!
24 = (log_2(15+P(9, 9)))!
24 = (15-(9-2))*sqrt(9)
24 = 15+2*9-9
24 = 15-(9-2*9)
24 = 15+9^2/9
24 = sqrt(9)-(15-C(9, 2))
24 = C(9, 2)-15+sqrt(9)
24 = C(9, 2)-(15-sqrt(9))
24 = C(9, 2)+sqrt(9)-15
24 = P(9-sqrt(9), 2)/15
24 = 2*(9*sqrt(9)-15)
24 = (15-9/sqrt(9))*2
24 = (9/sqrt(9))^2+15
24 = 9-15*(2-sqrt(9))
24 = 9-15/(2-sqrt(9))
24 = 15-(2-sqrt(9))*9
24 = 15-9/(2-sqrt(9))
24 = 15*(sqrt(9)-2)+9
24 = 15/(sqrt(9)-2)+9
24 = 15^(sqrt(9)-2)+9
24 = 15+9*(sqrt(9)-2)
24 = 15+9/(sqrt(9)-2)
24 = 15+9^(sqrt(9)-2)
24 = 15+C(9, sqrt(9)-2)
24 = 15+C(9, 2^sqrt(9))
24 = 15+P(9, 2^sqrt(9))
48 solution(s) in 74.951 seconds
1288 duplication(s)
7024936 combination(s)
--------------------
The program can enumerate all possible targets for given numbers.
Allow advanced operators?
Advanced operators disabled
Allow unary operator?
Unary operator disabled
Enumerate all target?y
Solve all targets
--------------------
Enter some numbers:1 2 3 4
-23 = 1-2*3*4
-22 = (1-3*4)*2
-21 = (1-2*4)*3
-20 = (1-2*3)*4
-19 = 1-(2+3)*4
-18 = (1-4)*2*3
-17 = 1-(2+4)*3
-16 = (1-2-3)*4
-15 = (1-2-4)*3
-14 = 2-(1+3)*4
-13 = 1-2-3*4
-12 = (1-2)*3*4
-11 = 2-1-3*4
-10 = 1*2-3*4
-9 = 1+2-3*4
-8 = 1-2-(3+4)
-7 = (1-2)*(3+4)
-6 = 2-1-(3+4)
-5 = 4-(1+2)*3
-4 = 1+2-(3+4)
-3 = (1+2)*(3-4)
-2 = 4-3-(1+2)
-1 = (1-2)*(4-3)
0 = (3-(1+2))*4
1 = (1-2)*(3-4)
2 = 1+2+3-4
3 = (1+2)*(4-3)
4 = 3+4-(1+2)
5 = (1+2)*3-4
6 = 1-2+3+4
7 = 4-(1-2)*3
8 = 3+4-(1-2)
9 = 3*4-(1+2)
10 = 1+2+3+4
11 = 1-2+3*4
12 = (2-1)*3*4
13 = (1+2)*3+4
14 = 1*2*(3+4)
15 = 1+2+3*4
16 = (3-(1-2))*4
17 = (1+4)*3+2
18 = (1*2+4)*3
19 = (2+3)*4-1
20 = (1*2+3)*4
21 = (1+2)*(3+4)
22 = 2*(3*4-1)
23 = 2*3*4-1
24 = (1+2+3)*4
25 = (1+4)*(2+3)
26 = (1+3*4)*2
27 = (1+2*4)*3
28 = (1+2*3)*4
30 = (1+4)*2*3
32 = (1+3)*2*4
36 = (1+2)*3*4
55 targets(s) in 0.304 seconds
30976 combination(s)
--------------------
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