Question 1
In how many ways can you reach any circle in the 10th row from the top circle if you can only move down-left or down-right and cannot pass through the black circle?
**Diagram convention:** The printed sketch shows only eight rows. Continue the same triangular pattern to row 10, counting the top circle as row 1. The forbidden circle is the middle circle of row 5. Different sequences of moves count as different paths, even if they end at the same circle. Enter the total number of paths as an integer.
**Diagram convention:** The printed sketch shows only eight rows. Continue the same triangular pattern to row 10, counting the top circle as row 1. The forbidden circle is the middle circle of row 5. Different sequences of moves count as different paths, even if they end at the same circle. Enter the total number of paths as an integer.