Everything Unique I I I III

Logic Level 4

A B C × D E F G H I \begin{array}{cccccc} & & & A & B & C\\ & \times & & & D & E\\ \hline & & F & G & H & I \end{array}

If all of those variables contain distinct positive single-digit integers, what can be said about the possible values of F G H I ‾ \overline{FGHI} ?

No solution exists. It must be odd. It can be either even or odd. It must be even.

Michael Huang by Michael Huang , 29, USA

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1 solution

Pi Han Goh
Feb 13, 2021

I don't think we can solve this by hand, but I hope to be wrong. 

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from itertools import permutations

for a,b,c,d,e,f,g,h,i in permutations('123456789'):
    ABC = int(a+b+c) ; DE = int(d + e) ; FGHI = int(f+g+h+i)
    if ABC * DE == FGHI:
        print(f"{ABC} x {DE} = {FGHI}")

'''Output:
138 x 42 = 5796
157 x 28 = 4396
159 x 48 = 7632
186 x 39 = 7254
198 x 27 = 5346
297 x 18 = 5346
483 x 12 = 5796
'''

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