Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

hard math problem?

The answer is not 20241.

How many positive integers less than one million has a digit sum of 20, and does not contain any two-digit substring whose digit sum is 7? For example, 123563 is one of those numbers while 435 and 123455 are not.

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  • atsuo
    Lv 6
    1 month ago

    You said "The answer is not 20241" , so what is your answer ? 

     

    I found that the answer was 20241 as the other answerers said . 

     

    If the numbers "07ABCD" , "007ABC" , "0007AB" and "00007A" are 

    rejected then 19908 becomes the answer . Is your answer 19908 ? 

     

    But they are not numbers with 6 digits so they may be counted . 

    For example , "007553" is "7553" so it must be counted .

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  • 1 month ago

    I wrote a PERL script to list all the possible integers matching your criteria.

    There are 20241 of them.

    Source(s): for $n (1..999999) { $sum = 0; for $i (1..length($n)) {$sum += substr($n,$i-1,1);} if ($sum eq 20) { $ok = 1; for $i (1..length($n)-1) {if (substr($n,$i-1,1)+substr($n,$i,1) eq 7) {$ok = 0;}} if ($ok eq 1) { print "$n\n"; ++$count; }}} print $count;
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  • 1 month ago

    Two people gave you that answer and I concur with their approach. I would like to see your working to explain why you think the answer is NOT 20241.

    Here's some pseudo code that will do the job:

    count = 0

    For i = 1 to 999999

    {

    - if DigSum(i) = 20

    - {

    --- if i contains '07', '16', '25', '34', '43', '52', '61' or '70' then break

    --- count = count + 1

    . }

    }

    print count

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