Working on patterns. There is a diagram. Its a rectangle with the numbers 10, 16, 23 in each corner. Inside the rectangle is a circle and inside the circle are the numbers 9, 12, 24. The directions say to place the numbers 8 to 26 either inside or outside the circle according to the pattern shown. Please help
To determine the pattern and figure out where to place the numbers 8 to 26, let's analyze the given diagram step by step.
First, let's look at the rectangle and the numbers in its corners: 10, 16, and 23. Notice that each corner number can be obtained by adding 6 to the previous corner number.
- Starting from 10 and adding 6, we get 10 + 6 = 16.
- Then, adding 6 to 16, we get 16 + 6 = 22.
- However, the given number in the last corner is 23, not 22. So, there might be an inconsistency or a different pattern emerging.
Next, let's observe the numbers inside the circle: 9, 12, and 24. These numbers do not follow the same pattern as the corner numbers.
Now, let's examine the overall diagram. Notice that if we subtract the number inside the circle from the corresponding corner number, we get a consistent pattern:
- For the top left corner: 10 - 9 = 1
- For the top right corner: 23 - 24 = -1
- For the bottom left corner: 16 - 12 = 4
From this pattern, it seems that we need to subtract the number inside the circle from the corresponding corner number and place the result either inside or outside the circle.
Now, let's apply this pattern to the numbers 8 to 26:
- For the number 8 inside the circle: From the top left corner, subtract 8 - 9 = -1. So, place -1 inside the circle.
- For the number 9 inside the circle: From the top right corner, subtract 9 - 24 = -15. Place -15 inside the circle.
- For the number 10 inside the circle: From the bottom left corner, subtract 10 - 12 = -2. Place -2 inside the circle.
Continue this process for the remaining numbers, placing a positive or negative result either inside or outside the circle based on the subtraction patterns.
Here is a breakdown of the calculations:
- 11 inside the circle: 11 - 9 = 2 (Place 2 outside the circle)
- 12 inside the circle: 12 - 12 = 0 (Place 0 inside the circle)
- 13 inside the circle: 13 - 24 = -11 (Place -11 outside the circle)
Repeat this process for all the numbers from 8 to 26, and place the results either inside or outside the circle accordingly.
By following this pattern, you should be able to correctly place the numbers 8 to 26 inside or outside the circle.