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Postman Problem

  • 22-05-2010 3:55pm
    #1
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,852 Mod ✭✭✭✭


    Here's a problem for you...(taken from the Irish Maths Olympiad 2009):

    Hamilton Avenue has eight houses. On one side of the street are the houses
    numbered 1,3,5,7 and directly opposite are houses 2,4,6,8 respectively. An
    eccentric postman starts deliveries at house 1 and delivers letters to each of
    the houses, Finally returning to house 1 for a cup of tea. Throughout the
    entire journey he must observe the following rules. The numbers of the houses
    delivered to must follow an odd-even-odd-even pattern throughout, each house
    except house 1 is visited exactly once (house 1 is visited twice) and the postman at no time is allowed to cross the road to the house directly opposite. How many different delivery sequences are possible?

    More kudos is going for a general method rather than trying all the possibilities...


Comments

  • #2
    ArmCandyBaby
    Closed Accounts Posts: 201 ✭✭ArmCandyBaby


    3*2*2*1*1*1*1 = 12

    That wouldn't pick up many attempt marks in an exam though...


  • #3
    CJC86
    Registered Users, Registered Users 2 Posts: 360 ✭✭CJC86


    ArmCandyBaby wrote: »
    3*2*2*1*1*1*1 = 12

    That wouldn't pick up many attempt marks in an exam though...

    I'm pretty sure it's more than that. What if the third visit was to House 2? Then clearly we would still have 2 options for the fourth visit.


  • #4
    ArmCandyBaby
    Closed Accounts Posts: 201 ✭✭ArmCandyBaby


    No I don't think so because if you go to house 2 third, then you will be left with two houses opposite each other that you still have to go to and there is only one way around that path OPPOSITE -> NOT OPPOSITE -> NOT OPPOSITE -> OPPOSITE.


  • #5
    CJC86
    Registered Users, Registered Users 2 Posts: 360 ✭✭CJC86


    Yes, that's right. Sorry, had briefly thought about it the day before, and I foolishly posted before checking whether I was right or not.


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