Question 110
Nela and Jane choose a positive integer $k$ and then play a game with a $9 \times 9$ table. Nela selects in every one of her moves one empty unit square and she writes $0$ to it. Jane writes $1$ to some empty (unit) square in every one of her moves. Furthermore, $k$ of Jane's moves follow each of Nela's moves and Nela starts. If the sum of numbers in each row and each column is odd at any time during the game, Jane wins. If the girls fill out the whole table (without Jane's win), Nela wins. Find the least $k$ such that Jane has a winning strategy. (Michal Rolínek)