Question 70
An $n$-type tiles triangle, where $n \geq 2$, is formed by the cells of a $(2n + 1) \times (2n + 1)$ array which are situated below its diagonals. For instance, a 3-type tiles triangle is the following:
Determine the maximal length of a sequence with pairwise distinct cells in an $n$-type tiles triangle, such that, beginning with the second one, any cell of the sequence has a common side with the previous one.
Determine the maximal length of a sequence with pairwise distinct cells in an $n$-type tiles triangle, such that, beginning with the second one, any cell of the sequence has a common side with the previous one.