Difficult Math Problem Based on Inversions Hard Fun HELP

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In summary, the conversation discusses the concept of inversions in a list of integers and how they change when the first integer is moved to the last position. The original arrangement has 38 inversions, but by moving the sixth smallest number to the last position, 15 inversions are eliminated and 14 new inversions are introduced, resulting in a total of 47 inversions.
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katek8k8
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Homework Statement


Given integers 4, 8, 7, 5. An inversion occurs when one integer is larger than an integer that follows it; thus, in the above arrangement there are two inversions due to 8 and one due to 7 or three inversions in all. There are twenty distinct possible integers arranged in some order with the sixth smallest in the first position. The number of inversions in this arrangement in 38. If the first integer is now moved to the last position, how many inversions are there in the new arrangement?



The Attempt at a Solution


Well if there are 38 inversions, and the sixth smallest number is first, that means there has to be 15 inversions following it in the pattern that would be eliminated by 5 if it were to move to the end of the list of numbers. That leads us to 33 inversions, but the problem still isn't complete.
Someone help PLEASE?
:)
 
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  • #2
If the sixth smallest number is first in the list, then there are 5 inversions due to that number being first in the list. By moving it to the end, we eliminate those 5 inversions. But by moving it to the end, we introduce 14 new inversions, caused by the 7th-20th hands having new inversions. So by moving this number to the right, we have created a net of nine new inversions. Nothing else changes, so our new number of inversions is 47.
 
  • #3
thank you SO much! that makes a lot of sense. i really appreciate it
 

1. What is a difficult math problem based on inversions?

A difficult math problem based on inversions is a type of mathematical puzzle that involves rearranging numbers or objects in a specific order or pattern. Inversions refer to the number of times two elements in a sequence are out of order. These types of problems often require critical thinking and use of various mathematical concepts and strategies to solve.

2. How can I approach solving a difficult math problem based on inversions?

One approach to solving a difficult math problem based on inversions is to break it down into smaller, more manageable parts. Analyze the given information and try to identify any patterns or relationships between the numbers or objects. Then, use different mathematical strategies such as trial and error, logical reasoning, or algebraic equations to find a solution.

3. What are some common mistakes people make when solving difficult math problems based on inversions?

One common mistake is not fully understanding the problem or jumping to conclusions without considering all the given information. Another mistake is not using the appropriate mathematical concepts or strategies to solve the problem. It is also important to double check the answer and make sure it satisfies all the given conditions.

4. How can I improve my problem-solving skills for difficult math problems based on inversions?

To improve your problem-solving skills for difficult math problems based on inversions, it is important to practice regularly and expose yourself to a variety of problems. This will help you become familiar with different problem-solving techniques and improve your critical thinking abilities. Working with a study group or seeking guidance from a teacher or tutor can also be helpful.

5. Are there any real-world applications for difficult math problems based on inversions?

Yes, difficult math problems based on inversions have various real-world applications in fields such as computer science, engineering, and finance. These problems can help with optimizing processes, designing algorithms, and solving complex equations. They also require skills such as pattern recognition and logical reasoning, which are essential in many professions.

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