Jump to content
BrainDen.com - Brain Teasers
  • 0

The broken clock


bonanova
 Share

Question

The minute hand of a clock was lost and had to be replaced. Unfortunately only some extra hour hands were available for use. At how many moments in a day did the repaired clock, with identical hour and minute hands, give an ambiguous time? (Assume AM and PM could be deduced by other means.)

Explanation: At noon (and midnight) the time was certain, even though the hands coincided.  Also, a few minutes after these times, in fact at most other times, it can be deduced which is the minute hand. But there are certain hand positions where that's not possible. How many ambiguous moments occur in the time interval [Midnight, Next Midnight)?

Link to comment
Share on other sites

10 answers to this question

Recommended Posts

  • 1
  Reveal hidden contents
Edited by Molly Mae
Link to comment
Share on other sites

  • 0

  Reveal hidden contents

Link to comment
Share on other sites

  • 0

In case it helps, here's a clarification and restatement of the question.

There are moments when it is not possible to identify which hand is the minute hand.
An "ambiguous moment" is when that fact makes the time uncertain.

How many ambiguous moments occur in any 24-hour period?

(Assume we always know the angles of the hands as accurately as needed.)

Link to comment
Share on other sites

  • 0
  Reveal hidden contents


 

  Reveal hidden contents

Edited by Molly Mae
Link to comment
Share on other sites

  • 0

Having second thoughts about your answer, or difficulty seeing it.

  Reveal hidden contents

 

Link to comment
Share on other sites

  • 0
  On 2/1/2018 at 5:42 PM, bonanova said:

Having second thoughts about your answer, or difficulty seeing it.

  Reveal hidden contents

 

Expand  

Yeah, I ended up taking it a step further and moving the minute hand by 1 degree at a time instead of the hour hand.  So the matching columns were a looooot longer.  I couldn't include it in the post because it was too long.

Edited by Molly Mae
Link to comment
Share on other sites

  • 0
  On 2/2/2018 at 7:51 AM, bonanova said:

Sounds good. FTW!

  Reveal hidden contents

 

Expand  
  Reveal hidden contents
Edited by Molly Mae
Link to comment
Share on other sites

  • 0

Sorry, I should have pointed out this was a thought experiment and all three hands are distinguishable.

  Reveal hidden contents

 

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...