1. **Problem statement:** We need to find the number of paths a checker can take from the bottom-center position to the top of the board, moving only diagonally upward. The checker can jump over squares containing an X. 2. **Understanding movement:** The checker moves diagonally upward left or right. If a square contains an X, the checker can jump over it to the next diagonal square beyond the X. 3. **Modeling the board:** Represent the board as a grid with rows and columns. The checker starts at the bottom row, center column. 4. **Counting paths without obstacles:** Normally, from each position, the checker can move to two positions diagonally above (left and right), so the number of paths doubles each row upward. 5. **Incorporating X jumps:** When an X is encountered diagonally adjacent, the checker must jump over it, landing two squares away diagonally. 6. **Dynamic programming approach:** Define $P(r,c)$ as the number of ways to reach position $(r,c)$. 7. **Base case:** At the bottom-center position, $P(0, center) = 1$. 8. **Transition:** For each position, sum the paths from possible previous positions considering jumps over Xs. 9. **Calculate paths row by row:** - For squares without X, $P(r,c) = P(r-1,c-1) + P(r-1,c+1)$. - For squares reachable by jumping over X, add $P(r-2,c-2)$ or $P(r-2,c+2)$ accordingly. 10. **Final answer:** Sum $P(top ext{ row}, c)$ for all columns $c$ at the top. Since the exact board size and X positions are not numerically specified, the exact number cannot be computed here. However, the method above allows calculation once the board details are known.