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The story

This story occurs not far from Liège, in Belgium.

We are January 1st, 2013. Two bad men prepare the attack of a train. To do this, they set an appointment, during the year, at 2:30 a.m., along the river Meuse. They both have a high precision, radio-controlled watch, and therefore always perfectly on time.

When the day comes, the first man does not sleep, and about 2:15 a.m. goes to the meeting place. He arrives at 2:30 a.m. precisely. He waits 15 minutes, finds that his companion has obviously forgotten the appointment, and goes home.

The second man was asleep. He wakes up abruptly during the night, finds that it is 2:15 a.m. and goes to the the meeting place. He arrives at 2:30 a.m. precisely. He waits 15 minutes, finds that his companion has obviously forgotten the appointment, and goes home.

Even today, several months after, the two men still do not understand what happened that night, how they could be in the same place and at the same time, without seeing each other, with watches perfectly on time.

The question

When (day and month) was that missed appointment ?

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It could be:

October, 27th

because:

Time change day! So when it's 3 A.M., it's actually 2 A.M. The first bad man is at the meeting at 2:30 A.M. old time (0:30 UTC), and the second one (who wakes up abruptly, remember) is at the meeting at 2:30 A.M. new time (so 3:30 A.M. old time (1:30 UTC), when the first man is probably at home, sleeping).

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    $\begingroup$ So, does daylight time “fall back” from 3AM to 2AM in Belgium (and Europe in general)? In the U.S. it’s 2AM → 1AM. $\endgroup$ – Peregrine Rook Dec 8 '16 at 21:40
  • $\begingroup$ @PeregrineRook Yes it does. $\endgroup$ – Benoit Dec 8 '16 at 22:31
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    $\begingroup$ @PeregrineRook In the countries in the European Union which have DST, the switch happens at 1:00 UTC, the last Sunday of October. In the Central European time zone (which includes Belgium and many other countries), this is 3:00 CEST → 2:00 CET. In the Western European time zone (e.g. UK, Ireland, Portugal), this is 2:00 WEST → 1:00 WET/GMT. (The spring switch happens at 1:00 UTC, last sunday of March.) $\endgroup$ – Paŭlo Ebermann Dec 11 '16 at 14:42
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They agreed to meet on

October 27th, 2013.

One bad man was at the specified place

when Daylight Savings Time was still active, so 0:30 UTC.

while the other bad man was there

when Daylight Savings Time was not active anymore, so 1:30 UTC.

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    $\begingroup$ +1 for referencing UTC values instead of "old time" and "new time" $\endgroup$ – Johannes Pille Dec 8 '16 at 11:39
  • $\begingroup$ First and correct answer, accepted. Congrats ! $\endgroup$ – Benoit Dec 8 '16 at 12:00
  • $\begingroup$ @Benoit thank you, but technically IAmInPLS was first (you can hover over the 'answered 1 hour ago' to see the exact timestamp), and IIRC there was a third answer as well (now deleted). Though I'm fairly sure we all three wrote our answers independently. $\endgroup$ – Glorfindel Dec 8 '16 at 12:02
  • $\begingroup$ @IAmInPLS Oups, sorry. Fixed. $\endgroup$ – Benoit Dec 8 '16 at 12:10
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As the owner of the question, I want to bring my own answer, and also think a bit about the implications of it. Of course the 2 already up-voted answers are perfectly correct.

Simply said, the solution is:

The first man is at the meeting point at 2:30 a.m. summer time, while the second man was at the same place at 2:30 a.m. winter time, on the same day.

But there is something really interesting to learn from this funny story (that could really occur, no magic involved here):

To specify a given point on the time line, it is most of the time sufficient to give the date (day,month,year) and time. Except if this point happens to be between 2:00 a.m. and 3:00 a.m. the last Sunday of October (the day we change from summer to winter time in Europe): in this particular case (and only in this case) you need extra info, whether it's still winter time or already summer time.

Think about it (sorry it may become a bit "technical"): As a software developer, I used to hear obvious assumptions like:

A day has 24 hours (Wrong! 27/10/2013 for instance has 25 hours)

Or:

The format string DD-MM-YYYY-HH24:mm:ss uniquely identifies a point in time (Wrong! "27-10-2013-02:30:00" is non-unique)

One last remark: For those adept of Geocaching (like me), I made a mystery cache out of the same story (in French only).

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