Calculate funny sums of cubes

numbers.py

# 166**3 + 500**3 + 333**3 = 166 500 333
# 296**3 + 584**3 + 415**3 = 296 584 415
# 710**3 + 656**3 + 413**3 = 710 656 413
# 828**3 + 538**3 + 472**3 = 828 538 472

# Executed in   18.47 mins
def f1():
    for i in range(100, 1000):
        for j in range(100, 1000):
            for k in range(100, 1000):
                s = i ** 3 + j ** 3 + k ** 3
                if f'{s}' == f'{i}{j}{k}':
                    print(i, j, k)

# Executed in  823.58 secs (13.72 mins)
def f2():
    for i in range(100, 1000):
        for j in range(100, 1000):
            for k in range(100, 1000):
                s = i ** 3 + j ** 3 + k ** 3
                if s % 1000 == k and f'{s}' == f'{i}{j}{k}':
                    print(i, j, k)

# Executed in  748.55 secs
def f3():
    for i in range(100, 1000):
        for j in range(100, 1000):
            for k in range(100, 1000):
                s = i ** 3 + j ** 3 + k ** 3
                x = s % 1000
                if x == k:
                    y = (s // 1000) % 1000
                    if y == j:
                        z = s // 1000000
                        if z == i:
                            print(i, j, k)

# Executed in  201.55 secs
def f4():
    for i in range(100, 1000):
        for j in range(i, 1000):
            for k in range(j, 1000):
                s = i ** 3 + j ** 3 + k ** 3

                x = s % 1000
                y = (s // 1000) % 1000
                z = s // 1000000

                if x ^ y ^ z ^ i ^ j ^ k == 0 and x + y + z == i + j + k:
                    p = min(x, y, z)
                    r = max(x, y, z)
                    q = x ^ y ^ z ^ p ^ r
                    if p == i and q == j and r == k:
                        print(z, y, x)

# Executed in   94.12 secs
def f5():
    from array import array
    qb = array('L', [i**3 for i in range(0, 1000)])

    for i in range(100, 1000):
        si = qb[i]
        for j in range(i, 1000):
            sj = si + qb[j]
            for k in range(j, 1000):
                s = sj + qb[k]

                x = s % 1000
                y = (s // 1000) % 1000
                z = s // 1000000

                if x ^ y ^ z ^ i ^ j ^ k == 0 and x + y + z == i + j + k:
                    p = min(x, y, z)
                    r = max(x, y, z)
                    q = x ^ y ^ z ^ p ^ r
                    if p == i and q == j and r == k:
                        print(z, y, x)

# Executed in   51.85 secs
def f6():
    from array import array
    qb = array('L', [i**3 for i in range(0, 1000)])

    for i in range(100, 1000):
        si = qb[i]
        for j in range(i, 1000):
            sj = si + qb[j]
            for k in range(j, 1000):
                s = sj + qb[k]

                x = s % 1000
                y = (s // 1000) % 1000
                z = s // 1000000

                if z < 1000 and x ^ y ^ z ^ i ^ j ^ k == 0 and x + y + z == i + j + k:
                    if qb[x] + qb[y] + qb[z] == s:
                        print(z, y, x)
                        

# Executed in   31.06 secs
def f7():
    from math import floor
    from array import array
    qb = array('L', [i**3 for i in range(0, 1000)])

    # We iterate over ordered triples i >= j >= k.
    # But i can't be too small or we will get a result with less than 9 digits.
    min_i = floor((10**8 / 3) ** (1/3))
    # i can't be too big either.
    # E.g. i = 999 => 999**3 + j**2 + k**3 > 997_002_999
    # We will get overflow (10 digits in a result) if the first triple is too large:
    #   i = 999, j >= 997, s > 999**3 + 997**3 > 10**9
    max_i = next(
        i for i in range(999, min_i, -1) if qb[qb[i] // 10**6] + qb[i] < 10**9)

    # (min_i, max_i) = (321, 880)
    for i in range(min_i, max_i+1):
        si = qb[i]
        # The same reasoning as above:
        #   when i is small, we need j and k be large enough to fill 9 digits.
        min_j = floor(((10**8 - si) / 2) ** (1/3)) if si < 10**8 else 100
        for j in range(min_j, i+1):
            sj = si + qb[j]
            for k in range(100, j+1):
                s = sj + qb[k]

                x = s % 1000
                y = (s // 1000) % 1000
                z = s // 1000000

                if z < 1000 and x ^ y ^ z ^ i ^ j ^ k == 0 and x + y + z == i + j + k:
                    if qb[x] + qb[y] + qb[z] == s:
                        print(z, y, x)