A cryptogram (part 3A)

Number Theory Level 4

$\begin{array} { l l l l l } & & A& B & C \\ + & & D & E & F \\ \hline & & G & H & I \\ \hline \\ \end{array}$

Now consider the above equation where different letter represents distinct digit from 1 to 9, $\overline{DEF} = 2\overline{ABC}$ and $\overline{GHI} = 3\overline{ABC}$ .

How many different solutions altogether?

1 6 2 3 0 5 4

1 solution

Nick Kent
May 25, 2019

Python script:

for i in range(1, 4):    
    for j in range(1, 10):    
        for k in range(1, 10):    
            n = 100*i + 10*j + k    
            st = set([i, j, k, (2*n)%10, (2*n//10)%10, (2*n//100)%10, (3*n)%10, (3*n//10)%10, (3*n//100)%10])    
            if len(st) == 9 and 0 not in st:    
                 print(n)

Result

I think the question was wrong because it didn't say anything about numbers with leading 0's, because then, we would've had 6 solutions.

Anonymous1 Assassin - 4 months, 1 week ago

A cryptogram (part 3A)

1 solution

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