.. blogpost::
    :title: Mathador
    :keywords: mathématiques, programmmation
    :date: 2022-12-08
    :categories: module

    Un petit problème de chiffre, le
    `mathador <https://maitressedelaforet.fr/le-mathador-rituel-de-calcul-mental/>`_
    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.

    ::

        # coding: utf-8
        from itertools import permutations

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

        solution = []
        parentheses = [(i, j) for i in range(0, 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...

    Résultats :

    ::

        28.0 (17-12/3+1)*2
        28.0 (17-(12)/3+1)*2
        28.0 ((17-12/3)+1)*2
        28.0 (17-(12/3)+1)*2
        28.0 (17-12/(3)+1)*2
        28.0 ((17-12/3)+1)*2
        28.0 ((17-12/3+1))*2
        28.0 (17-(12/3)+1)*2
        28.0 (17-12/(3+1))*2
        28.0 (17-(12/3)+1)*2
        28.0 (17-(12)/3+1)*2
        28.0 (17-(12/3)+1)*2
        28.0 (17-12/(3)+1)*2
        28.0 (17-12/(3+1))*2
        28.0 (17-12/(1+3))*2
        28.0 (17-12/(1+3))*2
        28.0 (17+3)*2-12/1
        28.0 ((17+3))*2-12/1
        28.0 ((17+3)*2)-12/1
        28.0 ((17+3)*2-12)/1
        28.0 ((17+3)*2)-12/1
        28.0 ((17+3)*2-12)/1
        28.0 (17+3)*2/1-12
        28.0 ((17+3))*2/1-12
        28.0 ((17+3)*2)/1-12
        28.0 ((17+3)*2/1)-12
        28.0 (17+3)*(2/1)-12
        28.0 ((17+3)*2)/1-12
        28.0 ((17+3)*2/1)-12
        28.0 (17+3)*(2/1)-12
        28.0 (17*(3+1)-12)/2
        28.0 (17*(3+1)-12)/2
        28.0 (17*(3+1)-12)/2
        28.0 (17*(3+1)-12)/2
        28.0 (17+3)/1*2-12
        28.0 (17+3/1)*2-12
        28.0 ((17+3))/1*2-12
        28.0 ((17+3)/1)*2-12
        28.0 ((17+3)/1*2)-12
        28.0 (17+(3)/1)*2-12
        28.0 ((17+3)/1)*2-12
        28.0 ((17+3/1))*2-12
        28.0 ((17+3/1)*2)-12
        28.0 (17+(3/1))*2-12
        28.0 ((17+3)/1*2)-12
        28.0 ((17+3/1)*2)-12
        28.0 (17+(3)/1)*2-12
        28.0 (17+(3/1))*2-12
        28.0 (17+1-12/3)*2
        28.0 ((17+1)-12/3)*2
        28.0 (17+(1)-12/3)*2
        28.0 (17+1-(12)/3)*2
        28.0 ((17+1)-12/3)*2
        28.0 ((17+1-12/3))*2
        28.0 (17+(1-12/3))*2
        28.0 (17+1-(12/3))*2
        28.0 (17+(1)-12/3)*2
        28.0 (17+(1-12/3))*2
        28.0 (17+1-(12)/3)*2
        28.0 (17+1-(12/3))*2
        28.0 (17*(1+3)-12)/2
        28.0 (17*(1+3)-12)/2
        28.0 (17*(1+3)-12)/2
        28.0 (17*(1+3)-12)/2
        28.0 (17/1+3)*2-12
        28.0 ((17/1)+3)*2-12
        28.0 (17/(1)+3)*2-12
        28.0 ((17/1)+3)*2-12
        28.0 ((17/1+3))*2-12
        28.0 ((17/1+3)*2)-12
        28.0 ((17/1+3)*2)-12
        28.0 (17/(1)+3)*2-12
        28.0 12*3+(1-17)/2
        28.0 (12*3)+(1-17)/2
        28.0 (12*3)+(1-17)/2
        28.0 12*3+((1-17))/2
        28.0 12/(1-3)+17*2
        28.0 (12/(1-3))+17*2
        28.0 (12/(1-3))+17*2
        28.0 12/((1-3))+17*2
        28.0 12/(1-3)+2*17
        28.0 (12/(1-3))+2*17
        28.0 (12/(1-3))+2*17
        28.0 12/((1-3))+2*17
        28.0 (3+17)*2-12/1
        28.0 ((3+17))*2-12/1
        28.0 ((3+17)*2)-12/1
        28.0 ((3+17)*2-12)/1
        28.0 ((3+17)*2)-12/1
        28.0 ((3+17)*2-12)/1
        28.0 (3+17)*2/1-12
        28.0 ((3+17))*2/1-12
        28.0 ((3+17)*2)/1-12
        28.0 ((3+17)*2/1)-12
        28.0 (3+17)*(2/1)-12
        28.0 ((3+17)*2)/1-12
        28.0 ((3+17)*2/1)-12
        28.0 (3+17)*(2/1)-12
        28.0 (3+17)/1*2-12
        28.0 (3+17/1)*2-12
        28.0 ((3+17))/1*2-12
        28.0 ((3+17)/1)*2-12
        28.0 ((3+17)/1*2)-12
        28.0 (3+(17)/1)*2-12
        28.0 ((3+17)/1)*2-12
        28.0 ((3+17/1))*2-12
        28.0 ((3+17/1)*2)-12
        28.0 (3+(17/1))*2-12
        28.0 ((3+17)/1*2)-12
        28.0 ((3+17/1)*2)-12
        28.0 (3+(17)/1)*2-12
        28.0 (3+(17/1))*2-12
        28.0 3*12+(1-17)/2
        28.0 (3*12)+(1-17)/2
        28.0 (3*12)+(1-17)/2
        28.0 3*12+((1-17))/2
        28.0 ((3+1)*17-12)/2
        28.0 ((3+1)*17-12)/2
        28.0 (3/1+17)*2-12
        28.0 ((3/1)+17)*2-12
        28.0 (3/(1)+17)*2-12
        28.0 ((3/1)+17)*2-12
        28.0 ((3/1+17))*2-12
        28.0 ((3/1+17)*2)-12
        28.0 ((3/1+17)*2)-12
        28.0 (3/(1)+17)*2-12
        28.0 2*(17+3)-12/1
        28.0 (2*(17+3))-12/1
        28.0 (2*(17+3)-12)/1
        28.0 (2*(17+3)-12)/1
        28.0 (2*(17+3))-12/1
        28.0 (2*(17+3)-12)/1
        28.0 2*((17+3))-12/1
        28.0 (2*(17+3)-12)/1
        28.0 2*(17+3)/1-12
        28.0 2*(17+3/1)-12
        28.0 (2*(17+3))/1-12
        28.0 (2*(17+3)/1)-12
        28.0 (2*(17+3)/1)-12
        28.0 (2*(17+3/1))-12
        28.0 (2*(17+3))/1-12
        28.0 (2*(17+3)/1)-12
        28.0 2*((17+3))/1-12
        28.0 2*((17+3)/1)-12
        28.0 2*(17+(3)/1)-12
        28.0 (2*(17+3)/1)-12
        28.0 (2*(17+3/1))-12
        28.0 2*((17+3)/1)-12
        28.0 2*((17+3/1))-12
        28.0 2*(17+(3/1))-12
        28.0 2*(17+(3)/1)-12
        28.0 2*(17+(3/1))-12
        28.0 2*(17/1+3)-12
        28.0 (2*(17/1+3))-12
        28.0 2*((17/1)+3)-12
        28.0 2*(17/(1)+3)-12
        28.0 (2*(17/1+3))-12
        28.0 2*((17/1)+3)-12
        28.0 2*((17/1+3))-12
        28.0 2*(17/(1)+3)-12
        28.0 2*(3+17)-12/1
        28.0 (2*(3+17))-12/1
        28.0 (2*(3+17)-12)/1
        28.0 (2*(3+17)-12)/1
        28.0 (2*(3+17))-12/1
        28.0 (2*(3+17)-12)/1
        28.0 2*((3+17))-12/1
        28.0 (2*(3+17)-12)/1
        28.0 2*(3+17)/1-12
        28.0 2*(3+17/1)-12
        28.0 (2*(3+17))/1-12
        28.0 (2*(3+17)/1)-12
        28.0 (2*(3+17)/1)-12
        28.0 (2*(3+17/1))-12
        28.0 (2*(3+17))/1-12
        28.0 (2*(3+17)/1)-12
        28.0 2*((3+17))/1-12
        28.0 2*((3+17)/1)-12
        28.0 2*(3+(17)/1)-12
        28.0 (2*(3+17)/1)-12
        28.0 (2*(3+17/1))-12
        28.0 2*((3+17)/1)-12
        28.0 2*((3+17/1))-12
        28.0 2*(3+(17/1))-12
        28.0 2*(3+(17)/1)-12
        28.0 2*(3+(17/1))-12
        28.0 2*(3/1+17)-12
        28.0 (2*(3/1+17))-12
        28.0 2*((3/1)+17)-12
        28.0 2*(3/(1)+17)-12
        28.0 (2*(3/1+17))-12
        28.0 2*((3/1)+17)-12
        28.0 2*((3/1+17))-12
        28.0 2*(3/(1)+17)-12
        28.0 2/1*(17+3)-12
        28.0 (2/1)*(17+3)-12
        28.0 (2/1*(17+3))-12
        28.0 (2/1)*(17+3)-12
        28.0 (2/1*(17+3))-12
        28.0 2/1*((17+3))-12
        28.0 2/1*(3+17)-12
        28.0 (2/1)*(3+17)-12
        28.0 (2/1*(3+17))-12
        28.0 (2/1)*(3+17)-12
        28.0 (2/1*(3+17))-12
        28.0 2/1*((3+17))-12
        28.0 (1+17-12/3)*2
        28.0 ((1+17)-12/3)*2
        28.0 (1+(17)-12/3)*2
        28.0 (1+17-(12)/3)*2
        28.0 ((1+17)-12/3)*2
        28.0 ((1+17-12/3))*2
        28.0 (1+(17-12/3))*2
        28.0 (1+17-(12/3))*2
        28.0 (1+(17)-12/3)*2
        28.0 (1+(17-12/3))*2
        28.0 (1+17-(12)/3)*2
        28.0 (1+17-(12/3))*2
        28.0 (1-17)/2+12*3
        28.0 ((1-17))/2+12*3
        28.0 ((1-17)/2)+12*3
        28.0 ((1-17)/2)+12*3
        28.0 (1-17)/2+3*12
        28.0 ((1-17))/2+3*12
        28.0 ((1-17)/2)+3*12
        28.0 ((1-17)/2)+3*12
        28.0 (1-12/3+17)*2
        28.0 (1-(12)/3+17)*2
        28.0 ((1-12/3)+17)*2
        28.0 (1-(12/3)+17)*2
        28.0 (1-12/(3)+17)*2
        28.0 ((1-12/3)+17)*2
        28.0 ((1-12/3+17))*2
        28.0 (1-(12/3)+17)*2
        28.0 (1-(12/3)+17)*2
        28.0 (1-(12)/3+17)*2
        28.0 (1-(12/3)+17)*2
        28.0 (1-12/(3)+17)*2
        28.0 ((1+3)*17-12)/2
        28.0 ((1+3)*17-12)/2