Question 32
If a sequence $\{a_1, a_2, \dots, a_n\}$ of positive integers (where $n$ is a positive integer) has the property that the last digit of $a_k$ is the same as the first digit of $a_{k+1}$ (here $k = 1, 2, \dots, n$ and we define $a_{n+1} = a_1$), then the sequence is said to be a 'dragon sequence'. For example, $\{414\}$, $\{208, 82\}$ and $\{1, 17, 73, 321\}$ are all 'dragon sequences'. At least how many two-digit numbers must be chosen at random to ensure that a 'dragon sequence' can be formed among some of the chosen numbers?