Try to solve the problem using combinatorics.

If the limit didn’t exist, the problem would be distributing <code>n</code> candies between <code>3</code> children.

The answer to the above problem would be <code>C(n + 2, 2)</code>.

Now try to combine this with the Inclusion-exclusion principle.

Apart from the above solution, there are other mathematical solutions that you can think of.