On Friday I posted this puzzle….

Fred leaves his house in the morning to go to his office.

Just as he is leaving he sees the reflection of his analog clock in the mirror.

Not realising that he is looking in a mirror, Fred assumes there is something wrong with the clock and rides his bike to work.

He arrives at the office 20 minutes later, and discovers that the office clock shows a time that is 2 hours and 30 minutes later than the time that he saw in the mirror image of his clock at home.

Assuming that the clock at Fred’s office and home were both set to the correct time, what time was it when he got to his office?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

Fred left home at 7:05 (saw 4.55 in the mirror), and arrived at his office at 7:25. Ten points to anyone who can provide the most elegant way of showing this is the case!

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle**(UKhere and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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I’m up early enough to say ‘Yeah’ , too early to attempt a concise explnanation, but here goes……two blind stabs in the dark leading to a logical conclusion

Alternative answer is that he leaves at 10.55pm. Mirror that is 1.05am, plus 20 minutes is 1.25am — 2.5 hours after he left. (maybe he’s working the late shift in a call centre 🙂 )

Easy to work out: you just need 65 minutes (half of 2 hours 10 minutes) either side of the vertical, plus 20 minutes on the right.

(maybe that’s not technically correct because Fred doesn’t leave in the morning, though he certainly _thinks_ he does)

He leaves at 10:55 am. That would work.

Nope, It is specified he leaves in the morning, in the puzzle, 10:55 pm cannot by any reasonable standard be referred to as “morning”. I first solved the puzzle this way too, perhaps because I find it easier to work with the top of the clockface in my head, but given the “morning” specified in the puzzle, I had to work it out for the “mirror” around the bottom of the clock (it makes sense that 7.05-7.25 is a reasonable time to go to work “in the morning”.)

And anyway, in this alternative solution he leaves at 01:05, but THINKS he leaves at 10:55 (sees 10:55 in the mirror) and arrives at 01:25

I got the same answer

but I assumed 1:05 pm he left home,i.e. he saw 10:55 in mirror

and reached at 1:25

Let x = real time he left home in min.

Let (x +20) = the real time he arrived at the office.

Let (720 -x) = reflected time in min (720 min = 12 hr0

150 min = 2 hr 30 min

(720 – x) + 150 = x + 20

870 – x = x + 20

850 = 2x

425 = x

x = 425 min

425 min = 7 hr 5 min (7:05)

720 – x = 720 – 425 = 295 min

295 min = 4 hr 55 min (4:55)

Solution

x + 0:20 = 7:05 + 0:20 = 7:25

He arrived at 7:25 AM

Nice!

Yet another answer is leaving at 07.35. Clock in mirror shows 05.25. 20 mins later clock shows 07.55 which is 2 hours 30 mins later than mirrored clock.

Another start time that works the same way is 1.05

7.35 in the mirror is 4.25, not 5.25.

I got the 10:55 answer but not the given one. Maybe that has something to do with the fact that I work graveyard shifts. 🙂

I listed envisaged actual leaving times between 6:00 and 8:00 then plotted

two lines: firstly 20 mins later, the second 2.5 hours later than the reflected leaving time. Where the two lines interescted gave me the answer as 7:05. Gold star and 10 points please.

Of course all these solutions ignore the mechanical asymmetry of a clock. A reasonable assumption given the magnitude of the effect and how tired Fred must be.

Oh snap, we’re not talking about digital clocks.

My thoughts entirely.

I took the word “show” literally (as opposed to “explain”). Here’s my modest attempt https://dl.dropbox.com/u/8113912/clocks.png

10 points!

I thought I was going mad! I had missed the words ‘analogue clock’ and I couldn’t work out what everyone else was on about!

the thing that confused me is that I assumed the mirror would be at 12 o’clock, not at 3 or 9, as the man would be holding his arm in front of him while standing in front of the mirror. What would be the solution in this case?

Dear Richard,

The time he arrived to his office in minutes is X

X=720-X+130 2X= 850 X=445 445 minutes = 7:25 This was the time he arrived to the office

Best wishes Dr. David Melumad

Dear Richard,

Sorry for the mistake

The time he left to his office in minutes is X The mirror image at this time is 720-X

The difference between them is the 130 minutes (2 and a half hour -20 minutes of his way to the office)

X-(720-X) =130 X-720+X = 130 2X= 850 X=425 425 minutes = 7:05 This was the time when he left to the office

Best wishes Dr. David Melumad

When he left the house, the ‘apparent’ time was 2:10 before the ‘actual’ – 2:30 – 0:20,

As the times were mirror images, they must be equal time intervals before and after 6:00 (since this all happened in the morning). Half of 2:10 is 1:05, and 1:05 before 6:00 is 4:55.

Sproz

Nice one Sprozmeister, except the question doesn’t say all events occurred in the morning – just that Fred leaves his house in the morning.

You need to apply your technique to 12 as well as to 6, giving a start time of 10.55 am, which is also in the morning.

Incidentally, this has been the best Friday Puzzle for ages. It takes a bit of working out, is not immediately obvious, can be calculated accurately, and is not spoiled by loads of dubious multi-interpretationalisms or spooling mistaeks.

I agree.

Nonetheless Richard only provided one of the possible answers.

I found the answer(s) for a digital clock: 02:10 or 12:11 on a non-military clock, and if it’s a military clock then 22:15 will also work.

For all those times, if you subtract 20 minutes and see them in the mirror, they will look the same as they were to begin with. Like this:

02:10 minus 20 minutes = 01:50 = 02:10 in the mirror

12:11 minus 20 minutes = 11:51 = 12:11 in the mirror

22:15 minus 20 minutes = 21:55 = 22:15 in the mirror

What’s a military clock?

I mean military time, i.e. a 24-hour clock, not 12-hour clock. So instead of 1pm it’s 13pm, instead of 5pm it’s 17pm, etc.

Sent from my Virgin Mobile Android-Powered Device

This puzzle requires the hour and minute hand to look the same, and they don’t on any clock that I know of. It’s a bit contrived because of that, though the actual working out of the answer once you realise you have to make that assumption is good fun.

Actually, that’s not the case here thinking about it! It does that with some other puzzles though.