Find a winning or a non-losing strategy for the following game: Consider $25$ sticks arranged in a $5$ x $5$ square. Players alternately take any number of sticks from a single row or column. At least one stick must be taken. There is an additional restriction that a group of sticks cannot be taken if the group contains a gap. The last person to move wins.
I was thinking that $A$ (first player) has a winning strategy if he goes first over $B$ (second player). I was thinking what if $A$ leaves $B$ with jan odd number of sticks. Wouldn't that be a setup for a win for $A$?
Can I get help with providing a logical argument on who has the winning strategy or non-losing strategy in this game? My friend and I were having a discussion about this problem after we saw this problem in E. Mendelson "Introducing Game Theory and its Applications". I said $A$ has a winning strategy but he said $B$ might have win therefore it is a non-losing strategy.
Can someone help me to prove this problem highlighted above with a convincing logical argument?