Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    --
    Offline

    14
    If you have 2 odd vertices, there is 1 pairing.
    If you have 4 odd vertices, there are 3 x 1 = 3 pairings (3 ways for one vertex, leaving the two vertices).
    If you have 6 odd vertices, there are 5 x 3 x 1 = 15 pairings (5 ways for one vertex, leaving four vertices which will recurse back to the previous line).

    Let the number of vertices be 2n and try writing this as a product.
    Offline

    14
    You need to be systematic, looking at (if the vertices are A,B,C,D,E,F): AB + others, AC + others, AD + others, AE + others and AF + others; deleting repetitions when they arise. But finding an individual number of pairings isn't important, it's the general rule in my previous post.

    If you have 2n vertices, then there will be 1 \times 3 \times 5 \times ... \times 2n-1 pairings. Try writing this as a quotient.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Are unpaid trial work shifts fair?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.