Speak now
Please Wait Image Converting Into Text...
Embark on a journey of knowledge! Take the quiz and earn valuable credits.
Challenge yourself and boost your learning! Start the quiz now to earn credits.
Unlock your potential! Begin the quiz, answer questions, and accumulate credits along the way.
Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
Turn Your Knowledge into Earnings.
I'm on a GCSE-a level syllabus currently, and I can't seem to think of any algebraic equation that I could comprise to solve this (with the GCSE/early a level syllabus). The question in full is
For which values of positive integer k is it possible to divide the first 3k positive integers into three groups with the same sum? (e.g. if k = 3, then the first 3k integers are 1,2,3,4,5,6,7,8,9. You can split these into 3 groups of 15, for example {{1,2,3,4,5},{7,8},{6,9}}. so it is possible for k=3)
Any help would be appreciated. Thanks
When I were a lad... we did lots of combinatorics at A-level. Shame it's gone, it's good grounding for a lot of university maths.
This is a nice example of applying algebra to combinatorics. Thank you for the question!
As a starter, consider the case where kk is even. In this case you can pair off numbers so they sum to k+1k+1 (and recall the story of Gauss being asked to sum the numbers 1 to 100). The number of pairs is still a multiple of 3 so group them any way you like!
Next consider the case k=3k=3. You have a solution to that in your question, but there are lots of other solutions. Ever seen the magic square?
So you can see there are various approaches to this sort of problem. It's good practice to explore!
Ok, for the general case where kk is odd. Let's do an example, with k=7k=7 to illustrate.
Write all your numbers in 3 rows.
No matter what stage you're at in your education or career, TuteeHub will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.
Course Queries 4 Answers
Course Queries 5 Answers
Course Queries 1 Answers
Course Queries 3 Answers
Ready to take your education and career to the next level? Register today and join our growing community of learners and professionals.