I could probably make a quick script to brute force it, but do you only need the solution? And what's it for? It doesn't look like anything meaningful will come out of those equations or those numbers.
EDIT: Unfortunately it's going to get a bit more complicated when you need every single solution. I'll have to withdraw my offer. I'd still be able to make it but it'd take more time than I can spare.
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but do you only need the solution
What do you mean?
Gothemasticator answered below 1 possible combination for each, so I'll take the first for example, 0+1+3+4=8 is the same for me as 1+0+3+4=8 or 4+1+0+3=8. It's not every single combinations possible but only those with different numbers (it can be 2 differents or all of them).
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A+B+C+D=8
0+1+3+4=8
A+B+C+D+E=-7
0+1+3+4+(-15)=-7
A+B+C+D+E=-21
(-8)+8+(-12)+12+(-21)=-21
A+B+C+D+E+F=18
(-8)+8+(-12)+12+17+1=18
Is it more difficult than I am making it? That pool of numbers with it's positive-negative pairs makes this easy.
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Do you need all the permutations?
I mean 0 + 1 + 3 + 4 = 8 and 4 + 3 + 1 + 0 = 8 should differ or not?
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That's for A + B + C + D = 8.
-27 + -14 + 20 + 29 = 8
-27 + -2 + 8 + 29 = 8
-27 + -2 + 17 + 20 = 8
-27 + 2 + 4 + 29 = 8
-27 + 3 + 12 + 20 = 8
-27 + 4 + 11 + 20 = 8
-21 + -12 + 12 + 29 = 8
-21 + -8 + 8 + 29 = 8
-21 + -8 + 17 + 20 = 8
-21 + -3 + 3 + 29 = 8
-21 + -3 + 12 + 20 = 8
-21 + -3 + 3 + 29 = 8
-21 + -3 + 12 + 20 = 8
-21 + -2 + 2 + 29 = 8
-21 + -2 + 11 + 20 = 8
-21 + 0 + 12 + 17 = 8
-21 + 1 + 8 + 20 = 8
-21 + 1 + 11 + 17 = 8
-21 + 4 + 8 + 17 = 8
-16 + -16 + 11 + 29 = 8
-16 + -8 + 3 + 29 = 8
-16 + -8 + 12 + 20 = 8
-16 + -7 + 2 + 29 = 8
-16 + -7 + 11 + 20 = 8
-16 + -7 + 2 + 29 = 8
-16 + -7 + 11 + 20 = 8
-16 + -3 + -2 + 29 = 8
-16 + -3 + -2 + 29 = 8
-16 + 0 + 4 + 20 = 8
-16 + 1 + 3 + 20 = 8
-16 + 1 + 11 + 12 = 8
-16 + 3 + 4 + 17 = 8
-16 + 4 + 8 + 12 = 8
-16 + -8 + 3 + 29 = 8
-16 + -8 + 12 + 20 = 8
-16 + -7 + 2 + 29 = 8
-16 + -7 + 11 + 20 = 8
-16 + -7 + 2 + 29 = 8
-16 + -7 + 11 + 20 = 8
-16 + -3 + -2 + 29 = 8
-16 + -3 + -2 + 29 = 8
-16 + 0 + 4 + 20 = 8
-16 + 1 + 3 + 20 = 8
-16 + 1 + 11 + 12 = 8
-16 + 3 + 4 + 17 = 8
-16 + 4 + 8 + 12 = 8
-15 + -14 + 8 + 29 = 8
-15 + -14 + 17 + 20 = 8
-15 + -8 + 2 + 29 = 8
-15 + -8 + 11 + 20 = 8
-15 + -7 + 1 + 29 = 8
-15 + -7 + 1 + 29 = 8
-15 + -3 + -3 + 29 = 8
-15 + -2 + 8 + 17 = 8
-15 + 0 + 3 + 20 = 8
-15 + 0 + 11 + 12 = 8
-15 + 1 + 2 + 20 = 8
-15 + 2 + 4 + 17 = 8
-15 + 3 + 8 + 12 = 8
-15 + 4 + 8 + 11 = 8
-15 + -14 + 8 + 29 = 8
-15 + -14 + 17 + 20 = 8
-15 + -8 + 2 + 29 = 8
-15 + -8 + 11 + 20 = 8
-15 + -7 + 1 + 29 = 8
-15 + -7 + 1 + 29 = 8
-15 + -3 + -3 + 29 = 8
-15 + -2 + 8 + 17 = 8
-15 + 0 + 3 + 20 = 8
-15 + 0 + 11 + 12 = 8
-15 + 1 + 2 + 20 = 8
-15 + 2 + 4 + 17 = 8
-15 + 3 + 8 + 12 = 8
-15 + 4 + 8 + 11 = 8
-14 + -8 + 1 + 29 = 8
-14 + -7 + 0 + 29 = 8
-14 + -7 + 12 + 17 = 8
-14 + -7 + 0 + 29 = 8
-14 + -7 + 12 + 17 = 8
-14 + -3 + 8 + 17 = 8
-14 + -3 + 8 + 17 = 8
-14 + -2 + 4 + 20 = 8
-14 + 0 + 2 + 20 = 8
-14 + 1 + 4 + 17 = 8
-14 + 2 + 3 + 17 = 8
-14 + 2 + 8 + 12 = 8
-14 + 3 + 8 + 11 = 8
-12 + -8 + 8 + 20 = 8
-12 + -8 + 11 + 17 = 8
-12 + -7 + -2 + 29 = 8
-12 + -7 + -2 + 29 = 8
-12 + -3 + 3 + 20 = 8
-12 + -3 + 11 + 12 = 8
-12 + -3 + 3 + 20 = 8
-12 + -3 + 11 + 12 = 8
-12 + -2 + 2 + 20 = 8
-12 + 0 + 3 + 17 = 8
-12 + 0 + 8 + 12 = 8
-12 + 1 + 2 + 17 = 8
-12 + 1 + 8 + 11 = 8
-8 + -7 + 3 + 20 = 8
-8 + -7 + 11 + 12 = 8
-8 + -7 + 3 + 20 = 8
-8 + -7 + 11 + 12 = 8
-8 + -3 + 2 + 17 = 8
-8 + -3 + 8 + 11 = 8
-8 + -3 + 2 + 17 = 8
-8 + -3 + 8 + 11 = 8
-8 + -2 + 1 + 17 = 8
-8 + 0 + 4 + 12 = 8
-8 + 1 + 3 + 12 = 8
-8 + 1 + 4 + 11 = 8
-8 + 2 + 3 + 11 = 8
-7 + -7 + 2 + 20 = 8
-7 + -3 + -2 + 20 = 8
-7 + -3 + 1 + 17 = 8
-7 + -3 + -2 + 20 = 8
-7 + -3 + 1 + 17 = 8
-7 + -2 + 0 + 17 = 8
-7 + 0 + 3 + 12 = 8
-7 + 0 + 4 + 11 = 8
-7 + 1 + 2 + 12 = 8
-7 + 1 + 3 + 11 = 8
-7 + 3 + 4 + 8 = 8
-7 + -3 + -2 + 20 = 8
-7 + -3 + 1 + 17 = 8
-7 + -3 + -2 + 20 = 8
-7 + -3 + 1 + 17 = 8
-7 + -2 + 0 + 17 = 8
-7 + 0 + 3 + 12 = 8
-7 + 0 + 4 + 11 = 8
-7 + 1 + 2 + 12 = 8
-7 + 1 + 3 + 11 = 8
-7 + 3 + 4 + 8 = 8
-3 + -3 + 2 + 12 = 8
-3 + -3 + 3 + 11 = 8
-3 + -2 + 1 + 12 = 8
-3 + -2 + 2 + 11 = 8
-3 + 0 + 3 + 8 = 8
-3 + 1 + 2 + 8 = 8
-3 + -2 + 1 + 12 = 8
-3 + -2 + 2 + 11 = 8
-3 + 0 + 3 + 8 = 8
-3 + 1 + 2 + 8 = 8
-2 + 0 + 2 + 8 = 8
0 + 1 + 3 + 4 = 8
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A + B + C + D + E = -7 -> https://pastebin.com/GspcU5ke
A + B + C + D + E = -21 -> https://pastebin.com/dQ2JdKV0
A + B + C + D + E + F = -18 -> https://pastebin.com/hXzUErmf
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I know nothing about coding and I'm pretty sure this can be easily done with some script or stuff like that.
My problem is that I would like to find all the combinations possible for this:
A+B+C+D=8
A+B+C+D+E= -7
A+B+C+D+E= -21
A+B+C+D+E+F= -18
ABCDEF are numbers from this pool: -27;-21;-16;-16;-15;-15;-14;-12;-8;-7;-7;-3;-3;-2;0;1;2;3;4;8;11;12;17;20;29.
They can be used only once for each equations and the equations are independent. (for example: "0" can be used in the 4 equations but only 1 time in each combination)
I already did by hand the combinations for 4 other equations but it takes hours and I probably missed some of them.
I hope I explained the problem well enough, ask me questions if not, so If anyone can help me with this, that would be awesome!
Edit: the pool of numbers is the same for each time, you can re-use a number in different combination.
Edit2: problem solved, thanks CrafterKolyan!!
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