I'm having trouble fully understanding this introductory combinatorics problem; this is all that's provided, so it's most likely me not fully comprehending the question.

Any help is appreciated.

The problem is this:

> 
> Each square of a 1998 by 2002 chess board contains either 0 or 1 such that the total number of squares containing 1 is odd in each row and each column. Prove that the number of white unit squares containing 1 is even.
> 
> 
> 

I have discovered that this is a legitimate question and has been copied out of a book entitled 102 Combinatorial Problems where the problem and solution are clearly stated [here](http://books.google.com/books?id=kdMilHngC4UC&pg=PA44&lpg=PA44&dq=Each+square+of+a+1998+by+2002+chess+board+contains+either+0+or+1+such+that+the+total+number+of+squares+containing+1+is+odd+in+each+row+and+each+column.+Prove+that+the+number+of+white+unit+squares+containing+1+is+even.&source=bl&ots=GSN6NgI2lx&sig=-rZubTL2fQDSMQDSg07IeHN-xxk&hl=en&sa=X&ei=m7y8U-PhKI3poATBzYG4Cw&ved=0CDEQ6AEwAg#v=onepage&q=Each%20square%20of%20a%201998%20by%202002%20chess%20board%20contains%20either%200%20or%201%20such%20that%20the%20total%20number%20of%20squares%20containing%201%20is%20odd%20in%20each%20row%20and%20each%20column.%20Prove%20that%20the%20number%20of%20white%20unit%20squares%20containing%201%20is%20even.&f=false).
Thank you and apologies for the ambiguity.