Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# hard math problem?

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

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

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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• 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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• 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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