A subset
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
of the set of integers 0 - 99 is said to have property
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
if it is impossible to fill a crossword-puzzle with 2 rows and 2 columns with numbers in
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
(0 is written as 00, 1 as 01, and so on). Determine the maximal number of elements in the set
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
with the property
%V0
A subset $S$ of the set of integers 0 - 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 the set $S$ with the property $A.$