The diagram below shows the method of construction of a book with four folded sheets in each
block, and three blocks in total. Page one is the first page of the first block of four sheets. At the
centre of each block, you can see the stitching that binds the book together.
A book is to be made using the same technique but with eight sheets of paper in each of the
three blocks.
Which of the following pairs of pages could be in the centre of a block (that is, if opened there,
the stitching would be visible)?
I don't really get why the answer's 48 and 49 here. And what is this type of problem called? I never get the gist of it.
The problem you mentioned is known as a booklet binding problem or book construction problem. It involves understanding how sheets of paper are folded and stitched to create a book.
In this specific problem, we are given a diagram that shows the construction of a book with four folded sheets in each block, and a total of three blocks. The center of each block is where the stitching is visible.
To solve the problem, we need to determine which pairs of pages could be in the center of a block if eight sheets of paper were used in each block.
In the original diagram, we can see that the pages in the center of the block are consecutive and follow a specific pattern. The first page of the center block is the last page of the previous block, and the second page of the center block is the first page of the next block.
Now, let's apply this pattern to the given problem with eight sheets of paper in each block.
If we have eight sheets in each block, there will be a total of 8 * 4 = 32 pages in each block.
In the first block, the last page would be page 32. Therefore, the first page of the second block would be 33, and the first page of the third block would be 65.
Now, let's check the options given:
Option 1: Pages 30 and 31 cannot be in the center of a block because they are not consecutive.
Option 2: Pages 48 and 49 can be in the center of a block. If we open the book at these pages, we would see the stitching.
Option 3: Pages 40 and 41 cannot be in the center of a block because they are not consecutive.
Option 4: Pages 60 and 61 cannot be in the center of a block because they are not consecutive.
Therefore, the correct answer is option 2, pages 48 and 49.
By understanding the pattern and applying it to the given problem, we can identify the correct pair of pages that would be in the center of the block.
I hope this explanation helps you understand the problem and its solution better!
To understand which pairs of pages could be in the center of a block, let's analyze the given information and the method of construction.
In the diagram, each block consists of four folded sheets, meaning there are eight pages in each block (front and back of each sheet). Additionally, there are three blocks in total.
When a book is constructed, it is stitched in the center of each block. Therefore, to find the pages that could be in the center, we need to determine the range of pages that fall within the stitching position.
In the original book construction, with four sheets in each block, the range of pages in the center block can be calculated as follows:
- First block: Pages 1 to 8
- Second block: Pages 9 to 16 (center block since it is stitched in the center)
- Third block: Pages 17 to 24
Now, considering the desired book construction with eight sheets in each block, we can find the range of pages in the center block as follows:
- First block: Pages 1 to 16
- Second block: Pages 17 to 32 (center block since it is stitched in the center)
- Third block: Pages 33 to 48
So, the center block for the book with eight sheets would include pages 17 to 32. Now, let's identify the pair of pages that could be in the center of the block:
- Page 48 and Page 49
By opening the book at page 48 and 49, the stitching that binds the book together would be visible, which satisfies the condition of being the center of the block.
This type of problem can be called a book construction problem or a stitching position problem, as it involves figuring out which pages would be visible if the book were opened at a specific point.
In summary, the pair of pages that could be in the center of a block in a book with eight sheets in each block is page 48 and 49.
There are 24 sheets of paper. Once they are stacked up, page 1 will be on the bottom left, and 24 sheets later, on top (the middle of the book when folded) there will be page 24 on the left (2 pages per sheet), and 49 on the right.
Ah, I see we have a bookworm in our midst. Let me shed some light on this stitching predicament of yours.
The diagram you mentioned shows the construction of a book with four folded sheets in each block and three blocks in total. In this case, the center of each block is where the stitching can be seen. Now, when it comes to a book with eight sheets in each block, we need to figure out which pairs of pages could be in the center.
To solve this, let's break it down. In each block, we have eight sheets, which means 16 pages. The first page of the block would be the outermost page on the left side, while the last page of the block would be the outermost page on the right side.
Considering this, let's take a look at the pair of pages 48 and 49. If these pages were in the center of a block, when opened, the stitching would be visible. Why? Because page 48 is the last page of the left block, and page 49 is the first page of the right block. The stitching would be right there in the middle, holding the whole thing together.
As for what this type of problem is called, it falls under the realm of logic puzzles or spatial reasoning. These puzzles often require you to analyze patterns, sequences, or configurations to find the right solution. It's like solving a little brain teaser to keep those neurons active.
So, there you have it! Page 48 and 49 would be the stitching-exposing pair in the center of a block. Happy reading and stitching spotting!