# Where will they strike?

You are part of an international anti-terror unit who has intelligence that some religious fanatics of the FSM church are going to soon blow a bomb in one or more of the world's major cities. You're shadowing their communication channels in the hope of learning of the exact plan early enough to prevent disaster.

To interfere, you have 5 super-secret-delta-swat units stationed in Berlin, Nairobi, Bogota, Singapore and Calgary. These units can relocate to any destination very quickly at a travel-speed of 500km/h (straight line). If they are at the scene of an attack, they supress it within 15min and are immediately ready to move again. They are in instant communication and can be ordered right from your location by a simple satellite call.

One night in late June, when you're in a cellar in Madrid at 04:00 in the morning you eavesdrop on a phone call apparently made from a cell phone in Lisbon (transcript below).

Jumping immediately to take appropriate actions you successfully managed to prevent disaster that day and become the unsung hero. (Whew!)

The puzzle question:

# What did you do and why?

This is the transcript of the phone call:

Lisbon HQ message. All units action as scheduled today.
Paris 17:30:45
Seoul 18:30:00
Denver 15:30:37
Tokyo 15:30:07
Omsk 18:30:37
Helsinki 21:30:22
Lima 16:30:45
Phoenix 13:00:30
Dallas 15:00:52
Rome 16:00:37
Cairo 19:00:45
Sydney 15:00:52
Perth 13:00:37
Gibraltar 17:30:37
Oslo 23:30:30
Melbourne 15:00:07
Port au Prince 14:30:07
Montreal 13:00:37
London 12:00:52
Athens 12:30:00
Cape Town 20:30:30
Brasilia 18:30:30
Karachi 11:30:00


# Notes

While this is a puzzle tagged as it is strictly logical and linked to the information provided above. I am not looking for some creative-story-telling solution. The second tag tells you where to solve the puzzle. The transcribed message indeed contains hidden information which made your decision uniquely clear. You have to decipher it.

Intermediate "work-in-progress" or "ideas" answers are welcome and will be commented on.

• Is this puzzle about how the 5 super secret teams will be directed to avoid destruction at any location? – CodeNewbie Jul 1 '15 at 16:40
• Are all times within the same timezone, or local time? Would it be too much of a hint if you told us? – Mark Jul 1 '15 at 16:55
• At this stage there are no additional hints, but a) you've received the message as described above - it is up to you how you interpret it. and b) You did prevent disaster. Whether you did it by sending the troupes out to one or more places or by other means is the puzzle, however, the message is (obviously) central to the puzzle and any solution must make sense of it. – BmyGuest Jul 1 '15 at 16:58
• Could this be related in any way to the leap-second that occurred in the last minute of the last day of last month, June? – itriedacrab Jul 1 '15 at 19:02
• @BmyGuest You mean northern hemisphere summer ;-) – Rand al'Thor Jul 1 '15 at 21:12

There's no bomb, the attack is canceled! We can just relay that message to our teams and relax.

We must find what the times in the given cities translate to in Lisbon, where the call was placed, using the map BmyGuest provided above. This gives us:

City        Zone    Lisbon Time
Paris           +2  16:30:45
Seoul           +9  10:30:00
Denver          -6  22:30:37
Tokyo           +9  07:30:07
Omsk            +6  13:30:37
Helsinki        +3  19:30:22
Lima            -5  22:30:45
Phoenix         -7  21:00:30
Dallas          -5  21:00:52
Rome            +2  15:00:37
Cairo           +2  18:00:45
Sydney          +10 06:00:52
Perth           +8  06:00:37
Gibraltar       +2  16:30:37
Oslo            +2  22:30:30
Melbourne       +10 06:00:07
Port au Prince  -4  19:30:07
Montreal        -4  18:00:37
London          +1  12:00:52
Athens          +3  10:30:00
Cape Town       +2  19:30:30
Brasilia        -3  22:30:30
Karachi         +5  07:30:00


What do we do next? EngineerToast and rand al'thor noticed that the values of the seconds divide a clock face into eighths. Now look at the possible hour+minute combinations, specifically the position of the hour hands at those times. These positions also divide the clock face into eighths! For example, at 13:30 (Omsk), the hour hand will be precisely one-eighth of the way around the clock.

The next question is what to do with two positions of hands on a clock (hour hand, second hand), given that both are in positions to the nearest eighth of a clock face. These signify flag semaphore! Treating the hour and second hand on the clock for each time as semaphore, we can read the following letters in order (i.e. 16:30:45, Paris, turns into S in semaphore): STILL NO BOMB, CANCEL ATTACK. That is the decryption, and we are done. Unless, of course, the letter is a lie meant to throw us off... But we're told we saved the day, so we're good :)

(Note: Dallas's given time should be 15:00:52, not 15:30:52.)

• Perfect, thanks for the Dallas correction, will edit in. – BmyGuest Jul 2 '15 at 5:08
• And welcome to the site! Great that he puzzle lured you here.(Did it?) – BmyGuest Jul 2 '15 at 5:09

To save someone else some time (Get it? Ha!), here are all the times translated to UTC:

City            Time        Zone    UTC Time
-----------------------------------------------
Lisbon           3:00:00     1       4:00:00

Paris           17:30:45     2      17:30:45
Seoul           18:30:00     10      10:30:00
Denver          15:30:37    -6      23:30:37
Tokyo           15:30:07     10      7:30:07
Omsk            18:30:37     7      13:30:37
Helsinki        21:30:22     3      20:30:22
Lima            16:30:45    -4      22:30:45
Phoenix         13:00:30    -6      21:00:30
Dallas          15:30:52    -4      21:30:52
Rome            16:00:37     2      16:00:37
Cairo           19:00:45     3      18:00:45
Sydney          15:00:52    11       6:00:52
Perth           13:00:37     9       6:00:37
Gibraltar       17:30:37     2      17:30:37
Oslo            23:30:30     3      22:30:30
Melbourne       15:00:07    11       6:00:07
Port au Prince  14:30:07    -3      19:30:07
Montreal        13:00:37    -3      18:00:37
London          12:00:52     1      13:00:52
Athens          12:30:00     3      11:30:00
Cape Town       20:30:30     3      19:30:30
Brasilia        18:30:30    -2      22:30:30
Karachi         11:30:00     6       7:30:00


Further observations:

• All the times have seconds values of 0,7,22,30,37,45, or 52. I don't see how this can be a coincidence unless OP was just lazy.
• Similarly, all of the minutes are either 0 or 30.
• The OP wasn't lazy ;-) And yes, time zones may come in handy... – BmyGuest Jul 1 '15 at 17:58
• Nice catch on the seconds and minutes! These must be encoding some useful info - I've updated my answer with a guess as to what it might be. cc @BmyGuest – Rand al'Thor Jul 1 '15 at 18:14
• Hmm, I've a slightly different time-zone info... I guess, because of DST. I've updated my question accordingly. – BmyGuest Jul 1 '15 at 18:51
• Ah! So the time zones do matter, then... – Engineer Toast Jul 1 '15 at 20:16

Assuming the times given are all in UTC (or some other uniform time zone - not local time), we can interpret each one as the time a unit is scheduled to leave that location for their single final destination.

The latest time is Oslo, so that should be closest to the final destination, which suggests you should mobilise the Berlin team.

We might be able to find the exact final destination and attack time by analysing all the times given and comparing ratios, but I won't spend ages doing this unless the OP says I'm looking in the right direction!

Scratch that. No feedback from the OP, so I'll assume it's completely wrong. (I've left it there though in case it gives someone else an idea).

Engineer Toast's observation on the seconds past each minute have given me an idea: the times 00, 07, 15, 22, 30, 37, 45, 52 (up to rounding error) divide the minute up into eighths, suggesting that the seconds column of the times denotes some variable that can take 8 different values. How about the compass directions north, east, south, west, northeast, northwest, southeast, southwest? Taking 00 to be north and proceeding clockwise, we get west from Paris, north from Seoul, southwest from Denver, northeast from Tokyo, and so on. Maybe lines drawn in these directions will spell out letters, if BmyGuest has pinched an idea from me ;-)

• Your second suggestion warrants a +1 ;c) Please note, that I've edited the original post and commented on Engineer's posting. The puzzle takes place in June ;c) – BmyGuest Jul 1 '15 at 18:55
• Should we consider the minutes 00 to be North and 30 to be South? That could give directions like North-NorthWest (NNW) and all the rest. Alternatively, the hours could represent a distance and the minutes simply modify it by $\frac{1}{2}$. – Engineer Toast Jul 1 '15 at 20:15
• I do not pinch ideas of others. That's a hint. I'm also editing in a (I think now obvious) tag to the puzzle. – BmyGuest Jul 1 '15 at 20:35