4. Dwarves Glóin, Óin, and Thráin found 70 identical precious stones and want to divide them among themselves so that each of them gets no less than 10 stones. In how many ways can the dwarves do this?
Answer: 861.

Solution: Give each dwarf 9 stones, and lay out the remaining 43 stones in a row. To distribute the remaining stones among the dwarves, it is sufficient to place two dividers in the 42 spaces between the stones. Gloin will receive the stones to the left of the first divider, Oin will receive the stones between the two dividers, and Thrain will receive the stones to the right of the second divider. The number of ways to place these two dividers is $\frac{42 \cdot 41}{2}=861$.

Comment: Deduct 1 point for a computational error with correct reasoning. Deduct 1-2 points for potentially useful but unimplemented ideas.