Question

Suppose you want to insert the number 3 into the list of numbers \(1,2,4,5,6,7\),

Short answer

Insert 3 between 2 and 4 to get the list \\(1, 2, 3, 4, 5, 6, 7\\).

Step-by-step solution

Identify the List Position

The list is \(1, 2, 4, 5, 6, 7\). First, identify where the number 3 should be placed to maintain the order. Since 3 is greater than 2 and less than 4, it should be placed between 2 and 4.

Insert the Number

Insert the number 3 into its correct position. The list becomes \(1, 2, 3, 4, 5, 6, 7\). This maintains the ascending order of the list.

Verify the Order

Ensure the list remains in numerical order after inserting the number. The final list \(1, 2, 3, 4, 5, 6, 7\) is in the correct ascending order.

Key concepts

Ordered Lists

Ordered lists are sequences where elements are arranged in a specific, non-random manner. Typically, this order is numerical or alphabetical for easy comprehension and retrieval. In an ordered list of numbers, you'll see each number placed in an increasing or decreasing arrangement.
To maintain the order of a list, each new element needs to be added in a way that the sequence remains intact. For instance, in the list \(1, 2, 4, 5, 6, 7\), inserting a number like 3 requires placing it between 2 and 4. This keeps the list in ascending order. The key to ordered lists is understanding the natural progression of numbers or items.

• Ordered lists make accessing information intuitive because you can predict where an item will be found based on its value.
• They are often used in situations where maintaining sequence is crucial, like in search algorithms or task priority settings.
• Inserting elements correctly into order lists requires careful checks to keep the arrangement consistent.

Algorithmic Thinking

Algorithmic thinking involves a step-by-step approach to solving problems or completing tasks. It's a way of understanding problems by breaking them down into manageable actions and decisions. When inserting a number into an ordered list, this process involves determining the correct position and then placing the number accordingly.
For example, inserting 3 into the list \(1, 2, 4, 5, 6, 7\) involves identifying where 3 fits based on its value relative to the other numbers. This positions 3 between 2 and 4. Algorithmic thinking breaks down the task into simple steps ensuring each move logically follows the last.

• Helps tackle complex problems by focusing on small, sequential tasks.
• Inserting in lists benefits from algorithmic thinking as it ensures accuracy and maintains order.
• The result of applying algorithmic thinking is a streamlined and efficient solution.

By practicing algorithmic thinking, students can improve their problem-solving skills significantly.

Problem-Solving Steps

Problem-solving is a crucial skill that follows a series of steps: understanding the problem, devising a plan, carrying out the plan, and evaluating the solution.
Inserting a number into an ordered list, like the example of placing 3 into \(1, 2, 4, 5, 6, 7\), is a classic problem-solving exercise.
The steps involved might include:

• Recognize the task: Identify that the insertion must maintain order.
• Develop a plan: Determine the right location for the new number.
• Execute the plan: Insert the number at the identified position.
• Review the outcome: Ensure the list remains in ascending order after insertion.

Following a structured approach makes complex tasks simple and efficient.
Each step builds on the last, ensuring clarity and precision in solutions.