IZhO 2008 Problem 3

Let $A = \{(a_1,\dots,a_8)|a_i\in\mathbb{N}$ , $1\leq a_i\leq i + 1$ for each $i = 1,2\dots,8\}$ .A subset $X\subset A$ is called sparse if for each two distinct elements $(a_1,\dots,a_8)$ , $(b_1,\dots,b_8)\in X$ ,there exist at least three indices $i$ ,such that $a_i\neq b_i$ . Find the maximal possible number of elements in a sparse subset of set $A$ .