Thanks Thanks:  0
Likes Likes:  0
Needs Pictures Needs Pictures:  0
Picture(s) thanks Picture(s) thanks:  0
Results 1 to 10 of 10
  1. 30th May 2011, 06:00 PM #1
    Greg Ward
    Greg Ward is offline GOLD MEMBER
    Join Date
    Feb 2005
    Location
    Sydney
    Age
    74
    Posts
    1,389

    Default It's raining and it's time

    When it's raining, too cold to glue and too wet in the shed and the timber outside is mouldy, it's time.

    Mr.Swan has promised to balance the Budget and is thinking about using some iron pyrites to assist, but Malcolm has found out and wants to check his future fund investment.

    There are 10 stacks of gold coins, each individual coin worth $10,000, each stack containing 10 coins. The coins are identical in size and appearance
    One entire stack is counterfeit, but you don't know which one.
    You know the weight of each genuine coin and you know the counterfeit coins are 10g heavier.
    You can weigh the coins as you wish on an electronic scale.

    What is the smallest number of weighings necessary to determine which stack is counterfeit?

    Greg
    Reply With Quote Reply With Quote
  2. 30th May 2011 06:00 PM # ADS
    Google Adsense Advertisement
    Join Date
    Always
    Location
    Advertising world
    Age
    2010
    Posts
    Many





     
  3. 30th May 2011, 06:20 PM #2
    Ironwood's Avatar
    Ironwood
    Ironwood is offline GOLD MEMBER
    Join Date
    Apr 2006
    Location
    near Mackay
    Age
    59
    Posts
    4,635

    Default

    I can see how to do it in 7 weighings.

    But you could be lucky and do it in 2 if you pick the counterfeit pile in your 1st or 2nd weigh.
    Reply With Quote Reply With Quote
  4. 30th May 2011, 06:38 PM #3
    ajw
    ajw is offline SENIOR MEMBER
    Join Date
    Jun 2007
    Location
    Blue Mountains
    Posts
    817

    Default

    Maximum of 5 weighs for my method:

    1. Weigh first 5 stacks in one go = x grams
    2. Weigh second 5 stacks in one go = y grams

    One group will be heavier, and can then calculate the average weight of a "real" stack.

    3. Divide heavier 5 stack into 2 groups: 2 stacks in one group, 3 in the other.
    4. Weigh first stack of 2. If this equals 2 "real" stacks, heavier fake stack must be in other 3. If not equal to 2 "real" stacks, weigh each of the two stacks to find the fake.

    5. Weigh any two of the 3 in the remaining group. If this equals 2 "real" stacks, fake is the other stack. If not, weigh either of the two to find which equals the "real" weight.

    ajw
    Reply With Quote Reply With Quote
  5. 30th May 2011, 06:47 PM #4
    _fly_'s Avatar
    _fly_
    _fly_ is offline GOLD MEMBER
    Join Date
    Apr 2011
    Location
    Dandenong, Vic
    Posts
    2,029

    Default

    Answer 3. 5 and 5 to find heavier side. Then 2 and 2, if even weight, its the fake left off the scales. If its one of the 2 sides, split that up to find heavier side. 9 piles you can do in 2 weighings.
    Reply With Quote Reply With Quote
  6. 30th May 2011, 06:50 PM #5
    Greg Ward
    Greg Ward is offline GOLD MEMBER
    Join Date
    Feb 2005
    Location
    Sydney
    Age
    74
    Posts
    1,389

    Default keep thinking.

    Not there yet....
    Greg
    Reply With Quote Reply With Quote
  7. 30th May 2011, 07:13 PM #6
    _fly_'s Avatar
    _fly_
    _fly_ is offline GOLD MEMBER
    Join Date
    Apr 2011
    Location
    Dandenong, Vic
    Posts
    2,029

    Default

    Rethink tells me its ONE weighing. One from first pile. 2 from second and so on. If you know the weight of one coin. Thats 55 coins in total. The amount that its over tells you which pile. If its over weight by 30 grams it pile 3. I knew I was a programmer for a reason.
    Reply With Quote Reply With Quote
  8. 30th May 2011, 07:16 PM #7
    Greg Ward
    Greg Ward is offline GOLD MEMBER
    Join Date
    Feb 2005
    Location
    Sydney
    Age
    74
    Posts
    1,389

    Default Too good

    Well done. Easy when you think about it.

    Greg
    Reply With Quote Reply With Quote
  9. 30th May 2011, 07:18 PM #8
    _fly_'s Avatar
    _fly_
    _fly_ is offline GOLD MEMBER
    Join Date
    Apr 2011
    Location
    Dandenong, Vic
    Posts
    2,029

    Default

    And I hated being wrong the first time. I would have sat up all night working it out.
    Reply With Quote Reply With Quote
  10. 30th May 2011, 07:24 PM #9
    Greg Ward
    Greg Ward is offline GOLD MEMBER
    Join Date
    Feb 2005
    Location
    Sydney
    Age
    74
    Posts
    1,389

    Default A more mathematical one coming

    OK. Time for a 'high school' maths problem. But I'll start a new thread.
    Greg
    Reply With Quote Reply With Quote
  11. 31st May 2011, 07:09 PM #10
    andrewr79
    andrewr79 is offline SENIOR MEMBER
    Join Date
    Jan 2011
    Location
    Sydney
    Posts
    613

    Default

    I still want that wood paneled 'like' button so I can give Fly some credit...clever thinking
    ---

    Visit my blog The Woodwork Geek to see what I've been up to or follow my ramblings on Twitter
    Reply With Quote Reply With Quote
« Previous Thread | Next Thread »

Similar Threads

  1. Raining inside the workshop!
    By Groggy in forum WOODWORK - GENERAL
    Replies: 23
    Last Post: 24th July 2007, 12:15 PM
  2. Shed work when it's raining?
    By RufflyRustic in forum WOODWORK - GENERAL
    Replies: 47
    Last Post: 14th January 2007, 10:50 AM
  3. Raining in Sydney
    By AlexS in forum NOTHING AT ALL TO DO WITH WOODWORK
    Replies: 19
    Last Post: 9th September 2006, 09:00 PM

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

Forum Rules