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 k is even. In this case you can pair off numbers so they sum to k+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=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 k is odd. Let's do an example, with k=7 to illustrate.
Write all your numbers in 3 rows.
manpreet![Tuteehub forum best answer]()
Best Answer
2 years ago
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
Any help would be appreciated. Thanks