Problem 61

p61.py

def is_cyclic(x,y):
    if (x % 100) == int(str(y // 100)):
        return True
    return False

def compute():
    tri = [(int(x*(x + 1)/2), "triangle") for x in range(1,1000) if 999 < x*(x + 1)/2 < 10000]
    sq = [(int(x*(x)), "square") for x in range(1,1000) if 999 < x*(x) < 10000]
    pen = [(int(x*(3*x - 1)/2), "pentagonal") for x in range(1,1000) if 999 < x*(3*x - 1)/2 < 10000]
    hexa = [(int(x*(2*x - 1)), "hexagonal") for x in range(1,1000) if 999 < (x*(2*x - 1)) < 10000]
    hep = [(int(x*(5*x - 3)/2), "heptagonal") for x in range(1,1000) if 999 < x*(5*x - 3)/2 < 10000]
    octa = [(int(x*(3*x - 2)), "octagonal") for x in range(1,1000) if 999 < x*(3*x - 2) < 10000]
    
    all_shapes = tri + sq + pen + hexa + hep + octa
    
    mydict = {}
    
    for x in all_shapes:
        mydict[x] = []
        for y in all_shapes:
            if x[0] != y[0] and x[1] != y[1]:
                if is_cyclic(x[0],y[0]):
                    mydict[x].append(y)
                 
    for a in octa:
        for b in mydict[a]:
            for c in mydict[b]:
                for d in mydict[c]:
                    for e in mydict[d]:
                        for f in mydict[e]:
                            if is_cyclic(f[0], a[0]):
                                if len(set([a[1],b[1],c[1],d[1],e[1],f[1]])) == 6:
                                    print([a[0],b[0],c[0],d[0],e[0],f[0]])
                                    return(sum([a[0],b[0],c[0],d[0],e[0],f[0]]))