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Re: the hourglass problem

Cross-posted to 4 groups.

Followups directed to: rec.puzzles

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William Elliot <marsh@rdrop.com> wrote:

> On Sun, 1 Jan 2012, root wrote:
>> RichD <r_delaney2001@yahoo.com> wrote:
> 
>>> You're given a 7 minute, and a 4 minute, sand
>>> hourglass.  Measure a 9 minute interval, in the first
>>> 9 minutes.  (no 'setup' period)
>>>
>>> ok, this is trivial.  But as computer nerds, we're
>>> interested in general solutions.  So, given hourglasses
>>> of n and m minutes:
>>>
>>> 1)  Can you devise a formula which generates a list of
>>>   all possible intervals produced by them?
> 
>> This problem is very interesting. After you realize
>> how to get 9 minutes, you then realize you are
>> able to get 4 minutes, 7 minutes, and then every
>> integer minute thereafter. So the numbers realizable
>> without delay are:
>> 4,7,8,9,10,11,12........
>>
> How did you realize 9, 10 and 11 without any delay?

The solution for 9 has already been posted multiple times.

10 and 11 are simple extensions of the solution for 9:

start both timers (t=0)
turn over the 4 minute timer when it expires (t=4)
turn over the 7 minute timer when it expires (t=7)
turn over both timers when the 4 minute timer expires (t=8)
turn over both timers when the 7 minute timer expires (t=9)
turn over both timers when the 4 minute timer expires (t=10)
turn over both timers when the 7 minute timer expires (t=11)
... and keep on marking every minute from 7 until you get bored.

> 
>> Then, clearly, with a 7 minute delay you can generate
>> every integer minute.
> 
> How can you generate 2 and 9 with only a 7 minute delay?

Same way you generate 9 and 16 with no delay.



-- 
Duncan Booth

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Thread

the hourglass problem RichD <r_delaney2001@yahoo.com> - 2011-12-31 18:03 -0800
  Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2011-12-31 19:21 -0800
    Re: the hourglass problem Dave Dodson <dave_and_darla@Juno.com> - 2011-12-31 19:41 -0800
      Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 19:48 -0800
        Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-01 20:44 -0800
          Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 23:08 -0800
            Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-02 07:55 -0800
              Re: the hourglass problem Dr Nick <3-nospam@temporary-address.org.uk> - 2012-01-02 16:17 +0000
                Re: the hourglass problem Robert Wessel <robertwessel2@yahoo.com> - 2012-01-03 03:37 -0600
    Re: the hourglass problem Remysun <remysun2000@yahoo.com> - 2012-01-02 17:10 -0800
      Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-03 01:12 +0000
  Re: the hourglass problem root <NoEMail@home.org> - 2012-01-01 05:51 +0000
    Re: the hourglass problem William Elliot <marsh@rdrop.com> - 2012-01-01 20:04 -0800
      Re: the hourglass problem Duncan Booth <duncan.booth@invalid.invalid> - 2012-01-02 11:42 +0000
    Re: the hourglass problem RichD <r_delaney2001@yahoo.com> - 2012-01-03 15:05 -0800
      Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-03 15:19 -0800
        Re: the hourglass problem PT <ptanenbaum@consultant.com> - 2012-01-04 12:28 -0800
          Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-04 13:44 -0800
        Re: the hourglass problem Dave Dodson <dave_and_darla@Juno.com> - 2012-01-04 22:55 -0800
          Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-04 23:55 -0800
            Re: the hourglass problem "Harry Vaderchi" <admin@127.0.0.1> - 2012-01-05 10:06 +0000
              Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-05 13:44 +0000
                Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-05 08:13 -0800
                Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 11:55 -0800
                Re: the hourglass problem JohnF <john@please.see.sig.for.email.com> - 2012-01-06 04:40 +0000
            Re: the hourglass problem Dave <dave_and_darla@Juno.com> - 2012-01-05 15:37 -0800
              Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 16:02 -0800
  Re: the hourglass problem Duncan Booth <duncan.booth@invalid.invalid> - 2012-01-02 11:50 +0000
  Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-02 17:18 +0000
    Re: the hourglass problem msb@vex.net (Mark Brader) - 2012-01-02 17:40 -0600
      Re: the hourglass problem RichD <r_delaney2001@yahoo.com> - 2012-01-02 17:37 -0800
        Re: the hourglass problem msb@vex.net (Mark Brader) - 2012-01-02 23:45 -0600
        Re: the hourglass problem "Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de> - 2012-01-03 10:06 +0100
        Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 12:51 +0100
          Re: the hourglass problem Nicolas Neuss <lastname@scipolis.de> - 2012-01-03 18:07 +0100
            Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 21:58 +0100
        Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-03 13:22 +0000
      Re: the hourglass problem "BartC" <bc@freeuk.com> - 2012-01-03 12:59 +0000
    Re: the hourglass problem Thomas Mlynarczyk <thomas@mlynarczyk-webdesign.de> - 2012-01-03 12:47 +0100
  Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-05 14:09 +0000
    Re: the hourglass problem Patricia Shanahan <pats@acm.org> - 2012-01-05 08:17 -0800
      Re: the hourglass problem Frederick Williams <freddywilliams@btinternet.com> - 2012-01-05 16:27 +0000
      Re: the hourglass problem Daniel Pitts <newsgroup.nospam@virtualinfinity.net> - 2012-01-05 11:57 -0800
      Re: the hourglass problem JohnF <john@please.see.sig.for.email.com> - 2012-01-06 06:42 +0000

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