Question 22
Twenty cubical blocks are arranged as shown. First, $10$ are arranged in a triangular pattern; then a layer of $6,$ arranged in a triangular pattern, is centered on the $10;$ then a layer of $3,$ arranged in a triangular pattern, is centered on the $6;$ and finally one block is centered on top of the third layer. The blocks in the bottom layer are numbered $1$ through $10$ in some order. Each block in layers $2,$ $3$ and $4$ is assigned the number which is the sum of the numbers assigned to the three blocks on which it rests. Find the smallest possible number which could be assigned to the top block.
