51. If there exist two numbers $\overline{a b}, \overline{b c} \in S$, then one can fill a crossword puzzle as $\left(\begin{array}{ll}a & b \\ b & c\end{array}\right)$. The converse is obvious. Hence the set $S$ has property $A$ if and only if the set of first digits and the set of second digits of numbers in $S$ are disjoint. Thus the maximum size of $S$ is 25 .
51. (SWE 4) A subset $S$ of the set of integers $0, \ldots .99$ is said to have property $A$ if it is impossible to fill a crossword puzzle with 2 rows and 2 columns with numbers in $S$ (0 is written as 00,1 as 01 , and so on). Determine the maximal number of elements in sets $S$ with property A.