In how many different ways can you arrange three 4x8 tiles to form a rectangle?
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Unless my interpretation of the question is faulty, I stand by my previous answer.
I think it comes down to interpretation. Looking at the previous answer, it looks like that the tiles are assumed to be square.
If the tiles are 4x8 (i.e. rectangular tiles), we would be able to form two different rectangles by piling them in different directions (4*24 or 8*12).
To find the number of different ways you can arrange the three 4x8 tiles to form a rectangle, we need to consider all the possible arrangements.
Let's break it down step by step:
Step 1: Start with one 4x8 tile. This can be arranged in only one way, forming a 4x8 rectangle.
Step 2: Add a second 4x8 tile. Now we have two tiles to arrange. We can place the second tile either horizontally or vertically to create a 4x16 rectangle or an 8x8 square.
Step 3: Add the third 4x8 tile. At this point, we have three tiles to arrange. There are several possibilities to consider:
- Case 1: If the first two tiles were placed horizontally, we can place the third tile horizontally, creating a 4x24 rectangle.
- Case 2: If the first two tiles were placed horizontally and the third tile is placed vertically, we can create a 4x16 rectangle with an 8x8 square on top.
- Case 3: If the first two tiles were placed vertically, we can place the third tile horizontally to create an 8x16 rectangle.
- Case 4: If the first two tiles were placed vertically and the third tile is placed vertically, we can create an 8x12 rectangle with a 4x8 rectangle on top.
Therefore, there are four different ways to arrange the three 4x8 tiles to form a rectangle.
In summary, the answer is four different ways.