How Often Did Sir Arcon's Time-Space Portal Open in a Day?

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Discussion Overview

The discussion revolves around the frequency with which Sir Arcon's time-space portal opens, based on the positions of the hands of a clock. Participants explore various interpretations of how many times the hands of a clock cross in a 24-hour period, considering different assumptions about the counting method.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the portal opens 24 times a day, assuming each hour represents a crossing.
  • Others argue for 25 openings, suggesting that the first hour counts as one crossing.
  • A different viewpoint suggests that the hands of the clock cross 22 times per day, noting that the hour hand's movement affects the timing of crossings, particularly around the 11 o'clock hour.
  • Some participants assert that there are 23 crossings, explaining that the crossing at 11 PM does not occur, leading to one less crossing in the total count.
  • One participant recounts a personal experience related to the misunderstanding of crossing times in a classroom setting, adding a historical context to the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as multiple competing views regarding the number of crossings remain, with estimates ranging from 22 to 25 times per day.

Contextual Notes

The discussion highlights the complexity of counting clock hand crossings, with participants relying on different assumptions and interpretations of the clock's behavior.

hemmul
Centuries ago, far from the mountains and the seas, in deep blue waters of the great pacific, right on an abandoned piece of holy land where the stormy sea touches cloudy sky, lived a powerful father of all magicians, his magesty sir Arcon von Zauberer. According to acient manuscriptes that reached us, sir Arcon was beleived to be a posessor of extremely weird watch. At a first glance it was a usual watch with two golden arrows (one counting hours, the other - minutes) that were marching smoothly and uniformly across the sparkling, silver background... However, each time the two arrows' positions, so as their directions, agreed (for example - at 12:00) - the famous gate to the time-space portal was opened, giving Arcon the only opportunity to travel through the whole universe...
Well, what he was doing during such trips, will perhaps remain a secret - right one of those that we are not ever to solve...
hmm... - unless one of davilla's or tribdog's encriptions spots some light on it ;)
The only thing that we can find out right away - is the number of his strange trips...
so, the question is:
How many times per day, did the gate open?

P.S. "brain teaser" for Greg: is it ok to post a new brain teaser, while there is at least one unanswered?
 
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I'm just going to guess. 24 times?
 
24 I agree. (assuming a day runs from 00:00 to 23:59)
 
25(assuming it runs from 12 AM to 12 PM)
 
25 times per day. Your starting hour counts as 1, so the first sweep around the watch gives you a count of 13. The second sweep will give you a count of 12.
 
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No, if the hands crossed 24 times a day that would be every hour on average. It's easy to see that, on account of the slow movement of the hour hand, it takes just a little over an hour between crossings: it takes an additional 5 minutes to make up for the hour mark, and then a little bit more to make up for the hour hand's movement during those 5 minutes (about 27 seconds, as it turns out).

Count it this way. The two hands of a clock cross once for every hour of the day except 11. After they cross just before 11:00, the minute hand doesn't catch up to the hour hand again until 12:00. So they cross 11 times every 12 hours, or 22 times per day, not counting the start of the next day.

My 6th grade teacher got upset with us because we refused to accept that the hands cross at exactly 1:05, 2:10, 3:15 etc. After all, they don't cross at 11:55!
 
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23 times a day. Same reason davilla gave but the first 12 hours there are 12 crosses :
midnight
approx 1:05
approx 2:10
.
.
.
approx 10:50
noon
approx 1:05
.
.
.
approx 10:50
then there is no crossing during the 11 o'clock PM hour so only one crossing is missed thus 23 crossings.
 
as davilla said, 22:

--------------------
midnight
approx 1:05
approx 2:10
......there are 11 of these
.
.
.
approx 10:50
-------------------
noon
approx 1:05
.
......there are 11 of these
.
approx 10:50
--------------------
 
I am going for 23 times. :) It crosses at 12am, but 24 hours later, that is the next day, so it does not count.
 
  • #10
and the winner is...
davilla!

davilla said:
Count it this way. The two hands of a clock cross once for every hour of the day except 11. After they cross just before 11:00, the minute hand doesn't catch up to the hour hand again until 12:00. So they cross 11 times every 12 hours, or 22 times per day, not counting the start of the next day.
excellent!
It seems that this problem was a piece of cake... it really was...next one ... is a bit more difficult ;)
 

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