Question 92
Let $n$ be a positive integer. Consider triples $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, \dots, $(x_n, y_n, z_n)$ which consist of integers $1, 2, \dots, 100$ and satisfy the following condition:
For all infinite sequences $a_1, a_2, \dots$ which consist of integers $1, 2, \dots, 100$, there exist a positive integer $i$ and an integer $j$ with $1 \le j \le n$ such that $(a_i, a_{i+1}, a_{i+2}) = (x_j, y_j, z_j)$.
Determine the minimum possible value of $n$.
For all infinite sequences $a_1, a_2, \dots$ which consist of integers $1, 2, \dots, 100$, there exist a positive integer $i$ and an integer $j$ with $1 \le j \le n$ such that $(a_i, a_{i+1}, a_{i+2}) = (x_j, y_j, z_j)$.
Determine the minimum possible value of $n$.