Multiplication in a 3×3 grid

arithmetic

If I place all the numbers from 1 to 9 in a 3×3 grid and I add the products of each row and column, then what is the minimal sum?enter image description here For example, the sum is 450 in the picture below.

Best Answer

import math
import itertools
def prod(l):
    r1 = l[0]*l[1]*l[2]
    r2 = l[3]*l[4]*l[5]
    r3 = l[6]*l[7]*l[8]
    c1 = l[0]*l[3]*l[6]
    c2 = l[1]*l[4]*l[7]
    c3 = l[2]*l[5]*l[8]
    return (r1+r2+r3+c1+c2+c3)

x = itertools.permutations([1,2,3,4,5,6,7,8,9])

minsum = math.inf

maxsum = 0

minlist = []
maxlist = []

for i in x:
    a = prod(i)
    if a < minsum:
        minlist = i
        minsum = a
    if a > maxsum:
        maxlist = i
        maxsum = a

print(minsum)
print(maxsum)
print(minlist)
print(maxlist)`

Not extremely enlightening but I ran this python code to find an answer of $436$, (and a max of $947$).

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