Question 6
Two sports teams, the Tigers and the Lions, each have $10$ members. Each team’s members are numbered $1$ to $10$ in increasing order of height. Form $10$ Tiger–Lion pairs, using everyone once. A pair is allowed if and only if the two numbers differ by at most $1$; for example Tiger $4$ can pair with Lions $3,4,5$. How many allowed pairings are there?