Question 36
Find the number of 20-tuples of integers $x_{1}, \ldots, x_{10}, y_{1}, \ldots, y_{10}$ with the following properties:
- $1 \leq x_{i} \leq 10$ and $1 \leq y_{i} \leq 10$ for each $i$;
- $x_{i} \leq x_{i+1}$ for $i=1, \ldots, 9$;
- if $x_{i}=x_{i+1}$, then $y_{i} \leq y_{i+1}$.
- $1 \leq x_{i} \leq 10$ and $1 \leq y_{i} \leq 10$ for each $i$;
- $x_{i} \leq x_{i+1}$ for $i=1, \ldots, 9$;
- if $x_{i}=x_{i+1}$, then $y_{i} \leq y_{i+1}$.