︠523173c8-24ef-4325-81ac-1af4c4ae2b2d︠
# 3 kupacos nim jatek
def lehetseges_lepesek(allas):
    (a, b, c) = allas
    L1 = [(x, b, c) for x in [0..a-1]]
    L2 = [(a, y, c) for y in [0..b-1]]
    L3 = [(a, b, z) for z in [0..c-1]]
    return L1 + L2 + L3
︡9e7fe127-c04b-4892-b7d6-c5a9f0a551eb︡{"done":true}
︠45acaa52-d89b-4bda-9b9b-068449d84cdfs︠
lehetseges_lepesek((5, 7, 2))
︡c3ed0238-1ae0-470b-9f93-b7725823565a︡{"stdout":"[(0, 7, 2), (1, 7, 2), (2, 7, 2), (3, 7, 2), (4, 7, 2), (5, 0, 2), (5, 1, 2), (5, 2, 2), (5, 3, 2), (5, 4, 2), (5, 5, 2), (5, 6, 2), (5, 7, 0), (5, 7, 1)]\n"}︡{"done":true}
︠431ea753-ba88-4dcb-8ba5-39cc97081284s︠
kiszamoltuk = {(0, 0, 0): false}
def nyertes_e(allas):
    if allas in kiszamoltuk:
        return kiszamoltuk[allas]
    for x in lehetseges_lepesek(allas):
        if not nyertes_e(x):
            kiszamoltuk[allas] = true
            return true
    kiszamoltuk[allas] = false
    return false
︡1d38f419-9446-4ba2-8b86-ac9150409753︡{"done":true}
︠83ab1b06-e1a3-48ab-8bf6-41c04749181ds︠
nyertes_e((3,3,0))
︡a2d2d835-1a37-46a8-9681-04bf866c2b35︡{"stdout":"False\n"}︡{"done":true}
︠5cb2c5e4-bc50-4cb4-8a26-3e314395e02fs︠
kiszamoltuk
︡84e2e622-6243-4d95-b1b4-3b0426d25910︡{"stdout":"{(3, 2, 0): True, (1, 1, 0): False, (2, 1, 0): True, (0, 2, 0): True, (0, 3, 0): True, (3, 1, 0): True, (3, 0, 0): True, (2, 2, 0): False, (1, 0, 0): True, (1, 2, 0): True, (0, 0, 0): False, (2, 3, 0): True, (3, 3, 0): False, (0, 1, 0): True, (1, 3, 0): True, (2, 0, 0): True}\n"}︡{"done":true}
︠733ee7f5-1730-451d-a4b4-47c871d46f00s︠
nyertes_e((20, 20, 20))
︡ff68bb55-5bed-4e9c-a138-4c0e0bd81b26︡{"stderr":"Error in lines 1-1\nTraceback (most recent call last):\n  File \"/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py\", line 1191, in execute\n    flags=compile_flags), namespace, locals)\n  File \"\", line 1, in <module>\nNameError: name 'nyertes_e' is not defined\n"}︡{"done":true}︡
︠9cc7171a-d53d-49a0-8186-401a3475bf52s︠
for a in [1..10]:
    for b in [1..10]:
        for c in [1..10]:
            if not nyertes_e((a,b,c)):
                print (a,b,c)
︡5a0b17d5-8e50-4384-9dd0-e83a06e3b1f1︡{"stdout":"(1, 2, 3)\n(1, 3, 2)\n(1, 4, 5)\n(1, 5, 4)\n(1, 6, 7)\n(1, 7, 6)\n(1, 8, 9)\n(1, 9, 8)\n(2, 1, 3)\n(2, 3, 1)\n(2, 4, 6)\n(2, 5, 7)\n(2, 6, 4)\n(2, 7, 5)\n(2, 8, 10)\n(2, 10, 8)\n(3, 1, 2)\n(3, 2, 1)\n(3, 4, 7)\n(3, 5, 6)\n(3, 6, 5)\n(3, 7, 4)\n(3, 9, 10)\n(3, 10, 9)\n(4, 1, 5)\n(4, 2, 6)\n(4, 3, 7)\n(4, 5, 1)\n(4, 6, 2)\n(4, 7, 3)\n(5, 1, 4)\n(5, 2, 7)\n(5, 3, 6)\n(5, 4, 1)\n(5, 6, 3)\n(5, 7, 2)\n(6, 1, 7)\n(6, 2, 4)\n(6, 3, 5)\n(6, 4, 2)\n(6, 5, 3)\n(6, 7, 1)\n(7, 1, 6)"}︡{"stdout":"\n(7, 2, 5)\n(7, 3, 4)\n(7, 4, 3)\n(7, 5, 2)\n(7, 6, 1)\n(8, 1, 9)\n(8, 2, 10)\n(8, 9, 1)\n(8, 10, 2)\n(9, 1, 8)\n(9, 3, 10)\n(9, 8, 1)\n(9, 10, 3)\n(10, 2, 8)\n(10, 3, 9)\n(10, 8, 2)\n(10, 9, 3)\n"}︡{"done":true}
︠1481945d-f484-4c7b-a16b-03492416f5d9s︠
# Számrejtvény (előáll-e 4 alapműv + zárójelből...)
# Mi volt a legbelső művelet? Csináljuk eggyel rövidebb listát
def lehetseges_elso(szamok):
    ret = []
    n = len(szamok)
    for i in [0..n-2]:
        for j in [i+1..n-1]:
            a, b = szamok[i], szamok[j]
            maradek = szamok[:i] + szamok[(i+1):j] + szamok[j+1:]
            belso_muvelet = [a+b, a-b, b-a, a*b]
            if b != 0:
                belso_muvelet += [a/b]
            if a != 0:
                belso_muvelet += [b/a]
            for x in belso_muvelet:
                ret += [[x] + maradek]
    return ret
︡ff8717d3-55fa-4889-874a-5bee1737dae2︡{"done":true}
︠9ec3f7cf-a8d4-48f5-b697-e7fd96f14411s︠
len(lehetseges_elso([2, 0, 8, 5]))
︡895aa57d-2988-4fc1-94d4-4be8615bf191︡{"stdout":"33\n"}︡{"done":true}
︠7f16a8c6-2086-49d5-8fa2-5554dd3e96c5s︠
def eloall_e(szamok, cel):
    ret = false
    if len(szamok) == 1:
        return szamok[0] == cel
    for x in lehetseges_elso(szamok):
        if eloall_e(x, cel):
            print x
            ret = true
    return ret
︡942027c2-30e0-4a59-b4c6-19385e5c73c2︡{"done":true}
︠79d7f5c9-1f0f-48cb-af3a-7b0e3b651b44s︠
eloall_e([1, 2, 3, 4], 10000)
︡511970b9-33d3-43ad-9ad3-1157ff456e87︡{"stdout":"False\n"}︡{"done":true}
︠4debed8c-bace-47a2-a53c-ee198ce0c1ffs︠
eloall_e([2, 3, 4, 5], 8)
︡7a28c5a8-52bb-4f6d-934c-553d248a5254︡{"stdout":"[8]\n[3, 5]\n[8]\n[4, 4]\n[8]\n[9, -1]\n[-1, 4, 5]\n[8]\n[-3, 5]\n[8]\n[3, 5]\n[8]\n[-4, 4]\n[8]\n[4, 4]\n[8]\n[9, 1]\n[1, 4, 5]\n[8]\n[3, 5]\n[8]\n[-3, 5]\n[8]\n[11, 3]\n[8]\n[-2, 6]\n[8]\n[2, 6]\n[6, 3, 5]\n[8]\n[4, 4]\n[8]\n[-4, 4]\n[8]\n[11, 3]\n[8]\n[-1, 7]\n[8]\n[1, 7]\n[7, 3, 4]\n[8]\n[1/2, 4]\n[5/2, 3, 4]\n[8]\n[-3, 5]\n[8]\n[3, 5]\n[8]\n[4, 2]\n[8]\n[-6, 2]\n[8]\n[6, 2]\n[8]\n[7, -1]\n[-1, 2, 5]\n[8]\n[3, 5]\n[8]\n[6, 2]\n[8]\n[4, 2]\n[8]\n[7, 1]\n[1, 2, 5]\n[8]\n[4, 4]\n[8]\n[4, 2]\n[8, 2, 4]\n[8]\n[-4, 4]\n[8]\n[4, 4]\n[8]\n[-4, 4]\n[8]\n[-6, 2]\n[8]\n[6, 2]\n[8]\n[6, -2]\n[-2, 2, 4]\n[8]\n[4, 4]\n[8]\n[4, 4]\n[8]\n[6, 2]\n[8]\n[6, 2]\n[2, 2, 4]\n[8]\n[11, 3]\n[8]\n[6, 2]\n[8]\n[-6, 2]\n[8]\n[-1, 9]\n[8]\n[1, 9]\n[9, 2, 3]\n[8]\n[4, 2]\n[-1, 2, 3]\n[8]\n[4, 2]\n[1, 2, 3]\nTrue\n"}︡{"done":true}
︠65495eee-2fcf-4a62-838f-4f65203faec8︠