Problem Analysis:
Let's analyze the given information step by step to find the number.

Step 1: Finding the tens digit:
- The tens digit is one more than the ones digit.
- The sum of the digits is 11.

Let's assume the ones digit as 'x', then the tens digit would be 'x+1'.
According to the given information, the sum of the digits is 11.
So, we can write the equation as:
x + (x+1) = 11
Simplifying the equation, we get:
2x + 1 = 11
Subtracting 1 from both sides:
2x = 10
Dividing both sides by 2:
x = 5

Therefore, the ones digit is 5 and the tens digit is 5+1=6.

Step 2: Finding the number:
- The number is larger than half of 100.
- The number is more than 6 tens and less than 7 tens.

Half of 100 is 100/2 = 50.
6 tens is 6 * 10 = 60.
7 tens is 7 * 10 = 70.

So, the number is larger than 50, more than 60, and less than 70.

Step 3: Combining the digits:
Now that we have the tens digit (6) and the ones digit (5), we can combine them to form the number.

Since the tens digit is placed before the ones digit, the number is 65.

Answer:
The number is 65.

What is a Pattern?
A pattern is a recurring or repetitive sequence of numbers, shapes, or objects that follows a certain rule or structure. Patterns can be found in various aspects of our daily lives, such as in mathematics, nature, art, and even in our behavior.

Types of Patterns:
1. Number Patterns: These patterns involve a sequence of numbers that follow a specific rule or relationship. For example, the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, ...) where each number is the sum of the two preceding numbers.

2. Geometric Patterns: These patterns involve a sequence of shapes or figures that follow a specific rule or relationship. For example, a tessellation pattern where a shape is repeated to completely cover a plane without any gaps or overlaps.

3. Visual Patterns: These patterns involve a sequence of visual elements such as colors, lines, or shapes that follow a specific rule or relationship. For example, a checkerboard pattern with alternating black and white squares.

4. Behavioral Patterns: These patterns involve a sequence of actions or behaviors that follow a specific rule or relationship. For example, a daily routine that includes waking up, brushing teeth, having breakfast, going to school or work, etc.

Importance of Patterns:
Patterns play a crucial role in various fields, including mathematics, science, technology, and art. They help us identify regularities, make predictions, solve problems, and understand the underlying structure of a system. Patterns also stimulate our cognitive abilities, enhance creativity, and improve our problem-solving skills.

In mathematics, patterns are used to study and describe relationships, formulate equations, and solve complex problems. They provide a foundation

Ans 63