Mr. Oakley, my wood shop teachger is kind of strange. He has a 12 inch strip of wood with only four marks in it that he uses as a ruler. Yesterday, I asked him about it. "What good is a ruler you use uf ut only has 4 marks on it? There are some lengths you can't measure!" "Nonsense, I have placed them in such a way that I can measure any whole number length from 1 to 12 inches between the marks;" "I will get you started on your one. One of the marks is one inch from the end."
Where should I place the other 3?
there are a lot of them but i chose 1, 4, 8,10
To solve this problem and determine where to place the other three marks on the ruler, we need to consider the given information and the requirement of being able to measure any whole number length from 1 to 12 inches.
First, let's analyze the given information:
- One of the marks is already placed one inch from the end.
Now, let's think about how to arrange the remaining three marks on the ruler to ensure we can measure any whole number length from 1 to 12 inches.
To achieve this, we can utilize the concept of symmetry. By placing the marks symmetrically around the center of the ruler, we can ensure that all possible whole number lengths are covered.
Here's a step-by-step method to place the other three marks:
1. Find the middle point of the ruler, which is 6 inches.
2. Place the second mark 1 inch to the left of the halfway point at 5 inches.
3. Place the third mark 1 inch to the right of the halfway point at 7 inches.
4. Place the fourth mark 1 inch to the left of the second mark at 4 inches.
By following these steps, you will have placed all four marks on the ruler in a way that allows you to measure any whole number length from 1 to 12 inches.
If you still have any queries or need further clarification, feel free to ask!