Arrangements

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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In a 3 by 3 grid, it is possible to place some counters on the grid so that there is an even number of counters in every row and every column. (We are taking zero as an even number.)

For which numbers of counters is this possible?

You may like to use this interactivity to explore your ideas.