Let's understand the tetromino puzzle. A tetromino consists of four unit squares connected along their edges. There are five basic tetromino shapes: I, O, L, T, and S. Our goal is to use exactly three tetrominoes to completely fill a 3 by 4 rectangle, with at least one being an S tile.
The S tetromino has a distinctive zigzag shape that creates specific placement constraints. In a 3 by 4 rectangle, there are only a few valid positions where an S tetromino can fit. Let's examine the main possible positions for the S tile within our target rectangle.
Now let's systematically test combinations. We need exactly 8 more squares after placing the S tetromino. Let's try different pairs of tetrominoes. After testing various combinations like S plus I plus L, we find that some arrangements leave gaps or overlaps. The solution that works is using one S tetromino and two L tetrominoes.
Here's our step-by-step solution. First, we place the S tetromino in the upper right area. Next, we add the first L tetromino along the left edge and top. Finally, we place the second L tetromino to fill the remaining space. The complete solution uses one S tetromino and two L tetrominoes to perfectly fill the 3 by 4 rectangle.
Let's verify our solution is correct. We have used exactly three tetrominoes: one S tetromino and two L tetrominoes. They completely fill the 3 by 4 rectangle with no gaps or overlaps. The requirement of using at least one S tile is satisfied. Therefore, the answer to the question 'What are the other two tiles?' is L and L.