A number is arranged in a pattern like: 12345678910111213141516...

What is the lowest value of that pattern divisible by 72?

They are single numbers, not seperate (i.e. first in sequence is 1, second is 12, third, 123 etc)

  • 1
    $\begingroup$ To be divisible by 72, it is necessary and sufficient for the number to be divisible by both 8 and 9. Do you know any way to tell if a number is divisible by 8 or by 9? $\endgroup$ – MJD Nov 26 '14 at 16:29

The first such numbers are $a_{36}$, $a_{44}$, $a_{144}$, $a_{152}$, $a_{216}$, ... So the lowest is $123\ldots343536$.

  • $\begingroup$ How would one go about finding those numbers without testing out every single instance though? $\endgroup$ – Isaac N Nov 27 '14 at 2:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.