`13` and `31` is a strange pair of numbers such that their squares `169` and `961` are also mirror images of each other. Find two more such pairs.

Answer

To find two more pairs of numbers whose squares are mirror images of each other, we can follow these steps:

### Step 1: Understand the concept of mirror images
Mirror images of numbers are those that appear reversed. For example, 13 and 31 are mirror images of each other. Their squares, 169 and 961, are also mirror images.

### Step 2: Identify a method to find pairs
We can start with a number, find its mirror image, and then calculate the squares of both numbers to check if their squares are mirror images.

### Step 3: Find the first pair
Let's start with the number 12:
- The mirror image of 12 is 21.
- Now, calculate the squares:
- \( 12^2 = 144 \)
- \( 21^2 = 441 \)

Since 144 and 441 are mirror images, we have found our first pair: **(12, 21)**.

### Step 4: Find the second pair
Now let's try with the number 102:
- The mirror image of 102 is 201.
- Now, calculate the squares:
- \( 102^2 = 10404 \)
- \( 201^2 = 40401 \)

Since 10404 and 40401 are mirror images, we have found our second pair: **(102, 201)**.

### Step 5: Verify other potential pairs
We can also check other numbers like 103 and its mirror image 301:
- Calculate the squares:
- \( 103^2 = 10609 \)
- \( 301^2 = 90601 \)

Since 10609 and 90601 are mirror images, we can consider this as a third pair: **(103, 301)**.

### Final Result
The pairs we found are:
1. (12, 21)
2. (102, 201)
3. (103, 301)