Suppose I have an integer, $m$, and another integer, $n$, then is there a way of working out how many numbers of length $n$ exist such that the sum of their individual digits is $m$?

Another way of thinking of this is how many ways are there of placing $m$ balls in a row of n buckets such that the first bucket is not empty and no bucket has more than $9$ balls.

Is there an explicit function that takes in the arguements $m$ and $n$ and outputs the answer or will an algorithm have to be implemented?

Thanks in advance


Your Answer

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

Browse other questions tagged or ask your own question.