Well done to Jeremy from the
Raffles Institution in Singapore for your well-reasoned solution:
It is only possible when there are 0, 4 or 6 counters.
Recognize that having an odd number of counters would result in a certain
number of rows and columns having an odd number of counters. With this
in mind, all examples with odd number of counters can be skipped.
When there are 0 counters, there are will be 0 counters on every square. (Remember zero is an even number!)
If only two counters are placed, at least 2 rows/columns would have an
odd number of counters as if two counters are placed in the same row, two
columns would have an odd number of counters and vice versa.
If 4 counters are placed, they can be placed in various positions, as long
as there is one empty row and column. If they are placed in 3 rows and columns, there would be certain rows/columns with an odd number of
Example, with counters in 3rows and 3 columns:
Example, with one row and one column empty:
6 is the most number of counters that can be placed as putting any more
would result in a line of 3. To do it, fill in all but one square in each
row and column.