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2 absent digits (Posted on 2020-11-28) Difficulty: 2 of 5
The product of 722*227 (163,894) contains neither 2 nor 7. List all the couples (b,c; b>c) such that the product bcc*ccb contains neither b nor c. Bonus: From the above list select couples, if any, using none of the corresponding digits in the partial products as well.

No Solution Yet Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

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Solution computer solution with an extension | Comment 3 of 6 |
for c=1:8
    for b=c+1:9
        bcc=100*b+11*c;
        ccb=110*c+b;
        p=num2str(bcc*ccb);
        good=true;
        for i=1:strlength(p)
            if str2num(p(i))==b || str2num(p(i))==c
                good=false;
                break
            end
        end
        if good
            disp([c b bcc ccb bcc*ccb])
        end
    end
end
disp(" ")
for b=1:8
    for c=b+1:9
        bcc=100*b+11*c;
        ccb=110*c+b;
        p=num2str(bcc*ccb);
        good=true;
        for i=1:strlength(p)
            if str2num(p(i))==b || str2num(p(i))==c
                good=false;
                break
            end
        end
        if good
            disp([c b bcc ccb bcc*ccb])
        end
    end
end

For problem as presented:

c  b    bcc   cbb     bcc*cbb
2  3    322   223       71806
2  7    722   227      163894
4  7    744   447      332568
5  8    855   558      477090
6  7    766   667      510922

For c>b (not in original problem):

5  2    255   552      140760
7  3    377   773      291421
7  4    477   774      369198
7  6    677   776      525352


  Posted by Charlie on 2020-11-28 12:30:37
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