Mathador, énigme à 4 opérations¶

Un petit problème de chiffre, le mathador consiste à trouver un montant à partir de 5 nombres et 4 opérations.

Example : composer 28 avec 17, 12, 3, 2, 1 et les opérations *, +, /, -.

Il faut tout utiliser.

C’est plus simple avec un programme, non ?

J’ai fait ça très vite. Il y a sans doute mieux.

0 (17-12/3+1)*2
0 (17-(12)/3+1)*2
0 ((17-12/3)+1)*2
0 (17-(12/3)+1)*2
0 (17-12/(3)+1)*2
0 ((17-12/3)+1)*2
0 ((17-12/3+1))*2
0 (17-(12/3)+1)*2
0 (17-12/(3+1))*2
0 (17-(12/3)+1)*2
0 (17-(12)/3+1)*2
0 (17-(12/3)+1)*2
0 (17-12/(3)+1)*2
0 (17-12/(3+1))*2
0 (17-12/(1+3))*2
0 (17-12/(1+3))*2
0 (17+3)*2-12/1
0 ((17+3))*2-12/1
0 ((17+3)*2)-12/1
0 ((17+3)*2-12)/1
0 ((17+3)*2)-12/1
0 ((17+3)*2-12)/1
0 (17+3)*2/1-12
0 ((17+3))*2/1-12
0 ((17+3)*2)/1-12
0 ((17+3)*2/1)-12
0 (17+3)*(2/1)-12
0 ((17+3)*2)/1-12
0 ((17+3)*2/1)-12
0 (17+3)*(2/1)-12
0 (17*(3+1)-12)/2
0 (17*(3+1)-12)/2
0 (17*(3+1)-12)/2
0 (17*(3+1)-12)/2
0 (17+3)/1*2-12
0 (17+3/1)*2-12
0 ((17+3))/1*2-12
0 ((17+3)/1)*2-12
0 ((17+3)/1*2)-12
0 (17+(3)/1)*2-12
0 ((17+3)/1)*2-12
0 ((17+3/1))*2-12
0 ((17+3/1)*2)-12
0 (17+(3/1))*2-12
0 ((17+3)/1*2)-12
0 ((17+3/1)*2)-12
0 (17+(3)/1)*2-12
0 (17+(3/1))*2-12
0 (17+1-12/3)*2
0 ((17+1)-12/3)*2
0 (17+(1)-12/3)*2
0 (17+1-(12)/3)*2
0 ((17+1)-12/3)*2
0 ((17+1-12/3))*2
0 (17+(1-12/3))*2
0 (17+1-(12/3))*2
0 (17+(1)-12/3)*2
0 (17+(1-12/3))*2
0 (17+1-(12)/3)*2
0 (17+1-(12/3))*2
0 (17*(1+3)-12)/2
0 (17*(1+3)-12)/2
0 (17*(1+3)-12)/2
0 (17*(1+3)-12)/2
0 (17/1+3)*2-12
0 ((17/1)+3)*2-12
0 (17/(1)+3)*2-12
0 ((17/1)+3)*2-12
0 ((17/1+3))*2-12
0 ((17/1+3)*2)-12
0 ((17/1+3)*2)-12
0 (17/(1)+3)*2-12
0 12*3+(1-17)/2
0 (12*3)+(1-17)/2
0 (12*3)+(1-17)/2
0 12*3+((1-17))/2
0 12/(1-3)+17*2
0 (12/(1-3))+17*2
0 (12/(1-3))+17*2
0 12/((1-3))+17*2
0 12/(1-3)+2*17
0 (12/(1-3))+2*17
0 (12/(1-3))+2*17
0 12/((1-3))+2*17
0 (3+17)*2-12/1
0 ((3+17))*2-12/1
0 ((3+17)*2)-12/1
0 ((3+17)*2-12)/1
0 ((3+17)*2)-12/1
0 ((3+17)*2-12)/1
0 (3+17)*2/1-12
0 ((3+17))*2/1-12
0 ((3+17)*2)/1-12
0 ((3+17)*2/1)-12
0 (3+17)*(2/1)-12
0 ((3+17)*2)/1-12
0 ((3+17)*2/1)-12
0 (3+17)*(2/1)-12
0 (3+17)/1*2-12
0 (3+17/1)*2-12
0 ((3+17))/1*2-12
0 ((3+17)/1)*2-12
0 ((3+17)/1*2)-12
0 (3+(17)/1)*2-12
0 ((3+17)/1)*2-12
0 ((3+17/1))*2-12
0 ((3+17/1)*2)-12
0 (3+(17/1))*2-12
0 ((3+17)/1*2)-12
0 ((3+17/1)*2)-12
0 (3+(17)/1)*2-12
0 (3+(17/1))*2-12
0 3*12+(1-17)/2
0 (3*12)+(1-17)/2
0 (3*12)+(1-17)/2
0 3*12+((1-17))/2
0 ((3+1)*17-12)/2
0 ((3+1)*17-12)/2
0 (3/1+17)*2-12
0 ((3/1)+17)*2-12
0 (3/(1)+17)*2-12
0 ((3/1)+17)*2-12
0 ((3/1+17))*2-12
0 ((3/1+17)*2)-12
0 ((3/1+17)*2)-12
0 (3/(1)+17)*2-12
0 2*(17+3)-12/1
0 (2*(17+3))-12/1
0 (2*(17+3)-12)/1
0 (2*(17+3)-12)/1
0 (2*(17+3))-12/1
0 (2*(17+3)-12)/1
0 2*((17+3))-12/1
0 (2*(17+3)-12)/1
0 2*(17+3)/1-12
0 2*(17+3/1)-12
0 (2*(17+3))/1-12
0 (2*(17+3)/1)-12
0 (2*(17+3)/1)-12
0 (2*(17+3/1))-12
0 (2*(17+3))/1-12
0 (2*(17+3)/1)-12
0 2*((17+3))/1-12
0 2*((17+3)/1)-12
0 2*(17+(3)/1)-12
0 (2*(17+3)/1)-12
0 (2*(17+3/1))-12
0 2*((17+3)/1)-12
0 2*((17+3/1))-12
0 2*(17+(3/1))-12
0 2*(17+(3)/1)-12
0 2*(17+(3/1))-12
0 2*(17/1+3)-12
0 (2*(17/1+3))-12
0 2*((17/1)+3)-12
0 2*(17/(1)+3)-12
0 (2*(17/1+3))-12
0 2*((17/1)+3)-12
0 2*((17/1+3))-12
0 2*(17/(1)+3)-12
0 2*(3+17)-12/1
0 (2*(3+17))-12/1
0 (2*(3+17)-12)/1
0 (2*(3+17)-12)/1
0 (2*(3+17))-12/1
0 (2*(3+17)-12)/1
0 2*((3+17))-12/1
0 (2*(3+17)-12)/1
0 2*(3+17)/1-12
0 2*(3+17/1)-12
0 (2*(3+17))/1-12
0 (2*(3+17)/1)-12
0 (2*(3+17)/1)-12
0 (2*(3+17/1))-12
0 (2*(3+17))/1-12
0 (2*(3+17)/1)-12
0 2*((3+17))/1-12
0 2*((3+17)/1)-12
0 2*(3+(17)/1)-12
0 (2*(3+17)/1)-12
0 (2*(3+17/1))-12
0 2*((3+17)/1)-12
0 2*((3+17/1))-12
0 2*(3+(17/1))-12
0 2*(3+(17)/1)-12
0 2*(3+(17/1))-12
0 2*(3/1+17)-12
0 (2*(3/1+17))-12
0 2*((3/1)+17)-12
0 2*(3/(1)+17)-12
0 (2*(3/1+17))-12
0 2*((3/1)+17)-12
0 2*((3/1+17))-12
0 2*(3/(1)+17)-12
0 2/1*(17+3)-12
0 (2/1)*(17+3)-12
0 (2/1*(17+3))-12
0 (2/1)*(17+3)-12
0 (2/1*(17+3))-12
0 2/1*((17+3))-12
0 2/1*(3+17)-12
0 (2/1)*(3+17)-12
0 (2/1*(3+17))-12
0 (2/1)*(3+17)-12
0 (2/1*(3+17))-12
0 2/1*((3+17))-12
0 (1+17-12/3)*2
0 ((1+17)-12/3)*2
0 (1+(17)-12/3)*2
0 (1+17-(12)/3)*2
0 ((1+17)-12/3)*2
0 ((1+17-12/3))*2
0 (1+(17-12/3))*2
0 (1+17-(12/3))*2
0 (1+(17)-12/3)*2
0 (1+(17-12/3))*2
0 (1+17-(12)/3)*2
0 (1+17-(12/3))*2
0 (1-17)/2+12*3
0 ((1-17))/2+12*3
0 ((1-17)/2)+12*3
0 ((1-17)/2)+12*3
0 (1-17)/2+3*12
0 ((1-17))/2+3*12
0 ((1-17)/2)+3*12
0 ((1-17)/2)+3*12
0 (1-12/3+17)*2
0 (1-(12)/3+17)*2
0 ((1-12/3)+17)*2
0 (1-(12/3)+17)*2
0 (1-12/(3)+17)*2
0 ((1-12/3)+17)*2
0 ((1-12/3+17))*2
0 (1-(12/3)+17)*2
0 (1-(12/3)+17)*2
0 (1-(12)/3+17)*2
0 (1-(12/3)+17)*2
0 (1-12/(3)+17)*2
0 ((1+3)*17-12)/2
0 ((1+3)*17-12)/2

from itertools import permutations

nombres = [17, 12, 3, 2, 1]
ops = ["+", "-", "/", "*"]
total = 28

solution = []
parentheses = [(i, j) for i in range(3) for j in range(i + 1, 4)]

# permutations sur les nombres
for pn in permutations(nombres):
    # permutations sur les opérations
    for po in permutations(ops):
        exp = []
        for d, o in zip(pn, po):
            exp.append(str(d))
            exp.append(str(o))
        exp.append(str(pn[-1]))

        # 0 parenthèse
        text = "".join(exp)
        res = eval(text)
        if res == 28:
            print(res)
            solution.append(res)

        # 2 parenthèses
        for i, j in parentheses:
            exp[i * 2] = "(" + exp[i * 2]
            exp[j * 2] = exp[j * 2] + ")"
            text = "".join(exp)
            try:
                res = eval(text)
                if res == 28:
                    print(res, text)
                    solution.append(res)
            except ZeroDivisionError:
                pass
            exp[i * 2] = exp[i * 2][1:]
            exp[j * 2] = exp[j * 2][:-1]

        # 4 parenthèses
        for a, b in parentheses:
            exp[a * 2] = "(" + exp[a * 2]
            exp[b * 2] = exp[b * 2] + ")"
            for c, d in parentheses:
                exp[c * 2] = "(" + exp[c * 2]
                exp[d * 2] = exp[d * 2] + ")"
                text = "".join(exp)
                try:
                    res = eval(text)
                    if res == 28:
                        print(res, text)
                        solution.append(res)
                except ZeroDivisionError:
                    pass
                exp[c * 2] = exp[c * 2][1:]
                exp[d * 2] = exp[d * 2][:-1]
            exp[a * 2] = exp[a * 2][1:]
            exp[b * 2] = exp[b * 2][:-1]

        # 6 parenthèses...

Total running time of the script: (0 minutes 1.677 seconds)

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