In a certain chess position, each row and each column contains an odd
number of pieces.
Prove that the total number of pieces on black squares is an even number.
Source: Proizvolov, “Problems Teaching Us How to Think".
(In reply to Parity Solution
by Brian Smith)
Would you care to erase your first sentence which is both wrong and irrelevant (the "certain chess position" implies standard labeling of the tiles i.e. the bottom left is black and called a1)?
Other than that, the solution is perfect and the rest of the text does not need any preamble.
If you do I would like to post it as an official solution, crediting you, of course.
Please reply ASAP.