VWO 2005

For all positive integers $n$ , find the remainder of $\dfrac{(7n)!}{7^n \cdot n!}$ upon division by 7.

We can obviously put 100 unit balls in a $10\times10\times1$ box. How can one put $105$ unit balls in? How can we put $106$ unit balls in?

If $n$ is an integer, then find all values of $n$ for which $\sqrt{n}+\sqrt{n+2005}$ is an integer as well.