Cryptograma

Number Theory Level 4

A B C D × B A D C B 6 D D D 6 B \Large \begin{array} {c c c c} &&& \color{#3D99F6}A & \color{#D61F06}B & \color{#EC7300}C &\color{#20A900}D \\ && \times & \color{#D61F06}B & \color{#3D99F6}A &\color{#20A900}D & \color{#EC7300}C \\ \hline \color{#D61F06}B & 6 &\color{#20A900}D &\color{#20A900}D &\color{#20A900}D & 6 & \color{#D61F06}B \\ \end{array}

For the cryptogram above, A A , B B , C C , and D D represent distinct digits.

Find A B ‾ × C D ‾ \overline{AB} \times \overline{CD} .

Note: x y ‾ ≠ x × y \overline{xy} \neq x \times y


The answer is 408.

Efren Medallo by Efren Medallo , 26, Philippines

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1 solution

Always can use code to solve this: 

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from itertools import permutations
for a,b,c,d in permutations('0123456789',4):
  if int(a+b+c+d)*int(b+a+d+c)==int(b+'6'+d+d+d+'6'+b):
    print(int(a+b)*int(c+d))


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Solution:
408

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