Maker and Breaker are building a wall. Maker has a supply of green cubical building blocks, and Breaker has a supply of red ones, all of the same size. On the ground, a row of $m$ squares has been marked in chalk as place-holders. Maker and Breaker now take turns in placing a block either directly on one of these squares, or on top of another block already in place, in such a way that the height of each column never exceeds $n$. Maker places the first block.
Maker bets that he can form a green row, i.e. all $m$ blocks at a certain height are green. Breaker bets that he can prevent Maker from achieving this. Determine all pairs $(m,n)$ of positive integers for which Maker can make sure he wins the bet.
1. **Initial Setup and Definitions:**
   - Maker and Breaker are playing a game on a grid of size \( m \times n \).
   - Maker's goal is to form a complete row of green blocks at some height \( y \).
   - Breaker's goal is to prevent Maker from achieving this.
   - Maker places the first block at \((1,1)\).

2. **Strategic Pairings:**
   - Maker uses a strategy based on pairing positions on the grid.
   - The pairings are defined as follows:
     \[
     (2i,1) \Leftrightarrow (2i+1,1) \quad \text{for} \quad i \in \{1, 2, \ldots, \frac{m-1}{2}\}
     \]
     \[
     (r,s) \Rightarrow (r,s+1) \quad \text{for} \quad r \in \{1, 2, \ldots, m\} \quad \text{and} \quad s \in \{1, 2, \ldots, n-1\}
     \]

3. **Maker's Strategy:**
   - Maker places the first green block at \((1,1)\).
   - Whenever Breaker places a red block at one of the paired positions, Maker places a green block at the other position in the pair.
   - This ensures that all blocks with coordinates \((x,y)\) where \(y\) is odd and greater than 1 will eventually be occupied by green blocks, provided the game continues.

4. **Ensuring a Green Row:**
   - By following the strategic pairings, Maker ensures that all positions \((x,3)\) will be occupied by green blocks.
   - This is because for every red block placed by Breaker, Maker can place a green block in the corresponding paired position, maintaining control over the odd rows.

5. **Conclusion:**
   - Maker can always ensure a complete row of green blocks at height \( y = 3 \) if \( m \) and \( n \) are both odd and greater than or equal to 3.

The final answer is \( \boxed{ (m, n) \text{ where } m \geq 3 \text{ and } n \geq 3 \text{ are odd numbers} } \).