A cryptogram (part 2)

Computer Science Level pending

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

In the above cryptogram, all the letters represent distinct digits from 0 to 9.

What is the minimum possible value of the 5-digit number F G H I J ‾ \overline{FGHIJ} ?

Note that A , C , F ≠ 0 A, C, F \neq 0 .


The answer is 15678.

Chan Lye Lee by Chan Lye Lee , 44, Singapore

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2 solutions

Hasmik Garyaka
Oct 22, 2017 
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def crypto():
    result=[]
    maxprod=100000
    for p in list(permutations(range(10))):
        if p[0]==0 or p[2]==0 or p[5]==0: continue
        ab=10*p[0]+p[1]
        cde=100*p[2]+10*p[3]+p[4]
        f=10000*p[5]+1000*p[6]+100*p[7]+10*p[8]+p[9]
        product=ab*cde
        if product>=100000 or product<10000:
            continue
        if product==f:
            if product<maxprod:
                result.append(p)
                print (product)
                maxprod=product
    print(result)

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Chan Lye Lee
May 15, 2017

It is a partial solution:

The following shows that F G H I J ‾ = 15678 \overline{FGHIJ} =15678 is possible. 3 9 × 4 0 2 1 5 6 7 8 \begin{array} { l l l l l } & & & 3 & 9 \\ \times & & 4 & 0 & 2 \\ \hline 1 & 5 & 6 & 7 & 8 \\ \hline \\ \end{array}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How did you solve this? Did you use computer assistance?

Pi Han Goh - 4 years ago

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Yes, by Excel.

Chan Lye Lee - 4 years ago

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Excel? I don't see how that's doable. Can you explain more in detail?

Like what do you write in the cells to "do all the trials"?

Pi Han Goh - 4 years ago

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