Answer the following questions by selecting the most appropriate option
Study the following pattern
`1 xx 1=1`
`11 xx 11=121`
`111 xx 111=12321`
What is `11111 xx 11111`?

Options

A. 123454321
B. 12345421
C. 123453421
D. 1234321

Answer

To solve the problem, we need to identify the pattern in the multiplication of numbers consisting of repeated '1's. Let's analyze the given examples step by step.

### Step 1: Analyze the Pattern
1. The first example is \( 1 \times 1 = 1 \).
2. The second example is \( 11 \times 11 = 121 \).
3. The third example is \( 111 \times 111 = 12321 \).

From these examples, we can see that:
- The product of \( 1 \) has one digit.
- The product of \( 11 \) has three digits (1, 2, 1).
- The product of \( 111 \) has five digits (1, 2, 3, 2, 1).

### Step 2: Identify the Next Case
Now, we need to find \( 11111 \times 11111 \).
- Following the established pattern, we can see that the number of digits in the result corresponds to the number of '1's in the multiplicands.
- For \( 11111 \) (which has 5 '1's), the result should have \( 2n - 1 \) digits, where \( n \) is the number of '1's. Thus, \( 2 \times 5 - 1 = 9 \) digits.

### Step 3: Construct the Result
The pattern in the results is:
- The first half of the digits counts up from 1 to 5.
- The second half counts down from 4 to 1.

So, the result should be:
- Counting up: 1, 2, 3, 4, 5
- Counting down: 4, 3, 2, 1

Combining these gives us \( 123454321 \).

### Final Answer
Thus, \( 11111 \times 11111 = 123454321 \).