# Two spies on a noisy train

Special agent Alex and deputy director Bob are traveling on the Trans-Siberian Railway. They need to set up a secret meeting in Vladivostok at the usual time, 18:30. The only thing to decide is the day of the week. To this end, and to annoy Alex, Bob insists on playing a Battleships guessing game on a 20x20 grid. The rows are indexed 1-20, and the columns are indexed A-T. In this game one should correctly guess the location of 4 row boats of size 1x1 and 4 destroyers of size 1x4.

Alex, while not really fond of this idea, agrees. The game starts at 14:06 in the afternoon, by Bob firing at H20, which is a miss. The game goes on for several hours. Alex eats a sandwich after move 107; Bob falls asleep after move 109 but a cigar he enjoys after move 111 puts him back on track. After a couple of additional moves he suddenly stands up and announces that he will get off of the train at the next stop in Krasnoyarsk. After saying goodbye, Bob, as a word of advice, suggests Alex to check his phone. Alex does so: the phone shows 18:03.

Which day of the week will the two meet again (for a possible rematch)?

Here are the guesses of Bob in the format XYZ where X and Y are obvious coordinates and m, h, and s are responses from Alex indicating miss, hit, or sink:

H20m, L9m, B9m, O16m, I16m, K9m, D9m, L3m, Q18m, J8m, K10m, J18m, T15m, H17m, J12m, N18m, L16m, Q19s, O11m, K7m, P8m, P20m, C8m, I8h, I9h, I10h, I11s, C9m, P11m, D10m, T10m, I3m, H6m, K13m, K14m, I19m, P16m, H13m, H8m, J20m, O18m, I17m, J15m, C11m, M8m, I2m, Q15m, E11m, K8m, J6m, S15m, A12m, L5m, S12m, Q12m, K5m, M20m, F12m, L6m, A10m, O15m, E10m, H4m, I20m, F10m, O14m, Q8m, B11m, B12m, H11m, P17m, M19m, T11m, S14m, H10m, F8m, K11m, H2m, J5m, R18h, R17h, R16h, R15s, L14m, K17m, M9m, H18m, L12m, N17m, T12m, A8m, N16m, N13m, E9m, P15m, D11m, L8m, M16m, T16m, S10m, L18m, S17m, Q13m, L7m, I5m, N9m, N11m, K1m, I14m, K4m, S13m, K2m, H19m, R8m, S20m, B8m, T8m, H3m, J17m, I12m, J13m, T9m, O12m, Q10m, J1m.

And here are the guesses of Alex:

P1m, J20m, C12m, M9m, K19m, M18m, B4s, E5m, N8m, T1m, M6m, T5m,G13m, L5m, J18m, G17m, S8s, G7m, A18m, G18m, K4m, D2m, A16m, M5m,T3m, I9m, O10m, J5m, M7m, B8m, I14m, L12m, A5m, G5m, N5m, P15m, D4m, N18m, D12m, T2m, K15m, T10m, F4m, E3m, I11m, E15m, P10m, E16m, T6m, G2m, S6m, G6m, M1m, S9m, Q2m, P3m, Q4m, L15m, B17m, I20m, K12m, F7m, R14m, B6m, H12m, R18m, J6m, N20m, L18m, D3m, C19m, G9m, J1m, R8m, E11m, N13m, H3m, B7m, Q3m, I4m, A10m, Q13m, J14m, E13m, L1m, C20m, O12m, R13m, A7m, T15m, C3m, L20m, R15m, C5m, P11m, B12m, H5m, O4m, C16m, O1m, F12m, G3m, N6m, E14m, F8m, M19m, M17s, N11m, L16m, R20m, T13m, R2m, M2m, D16m, L9m, C14m, T17m, Q7m, H6m, O8m, P20m, P18m, D7m, B11m.

The day of the next meeting is:

Monday

Simulating the game between Bob and Alex, the final boards look like this (left is Bob's board, right is Alex's:

   A B C D E F G H I J K L M N O P Q R S T      A B C D E F G H I J K L M N O P Q R S T
1 . . . . . . . . . m m . . . . . . . . .    1 . . . . . . . . . m . m m . m m . . . m
2 . . . . . . . m m . m . . . . . . . . .    2 . . . m . . m . . . . . m . . . m m . m
3 . . . . . . . m m . . m . . . . . . . .    3 . . m m m . m m . . . . . . . m m . . m
4 . . . . . . . m . . m . . . . . . . . .    4 . s . m . m . . m . m . . . m . m . . .
5 . . . . . . . . m m m m . . . . . . . .    5 m . m . m . m m . m . m m m . . . . . m
6 . . . . . . . m . m . m . . . . . . . .    6 . m . . . . m m . m . . m m . . . . m m
7 . . . . . . . . . . m m . . . . . . . .    7 m m . m . m m . . . . . m . . . m . . .
8 m m m . . m . m h m m m m . . m m m . m    8 . m . . . m . . . . . . . m m . . m s .
9 . m m m m . . . h . m m m m . . . . . m    9 . . . . . . m . m . . m m . . . . . m .
10 m . . m m m . m h . m . . . . . m . m m   10 m . . . . . . . . . . . . . m m . . . m
11 . m m m m . . m s . m . . m m m . . . m   11 . m . . m . . . m . . . . m . m . . . .
12 m m . . . m . . m m . m . . m . m . m m   12 . m m m . m . m . . m m . . m . . . . .
13 . . . . . . . m . m m . . m . . m . m .   13 . . . . m . m . . . . . . m . . m m . m
14 . . . . . . . . m . m m . . m . . . m .   14 . . m . m . . . m m . . . . . . . m . .
15 . . . . . . . . . m . . . . m m m s m m   15 . . . . m . . . . . m m . . . m . m . m
16 . . . . . . . . m . . m m m m m . h . m   16 m . m m m . . . . . . m . . . . . . . .
17 . . . . . . . m m m m . . m . m . h m .   17 . m . . . . m . . . . . s . . . . . . m
18 . . . . . . . m . m . m . m m . m h . .   18 m . . . . . m . . m . m m m . m . m . .
19 . . . . . . . m m . . . m . . . s . . .   19 . . m . . . . . . . m . m . . . . . . .
20 . . . . . . . m m m . . m . . m . . m .   20 . . m . . . . . m m . m . m . m . m . .

I noticed right away that Bob's board was filled out in an odd manner. It's not quite the right format to be a QR code, but it is very close. (Thanks to 2012rcampion for pointing this out.) By adding one row to the left and top, and placing the position indicators in the three gaps, we get this (drawing boxes instead of letters):

"Alex, check your phone." ~Bob, 2016

My phone to decoded the message within the QR code: MONDAY. So, that is our answer.

The following are simply extraneous information:

- times
- actions (eating a sandwich, smoking a cigar, taking a nap), and their corresponding turns
- the types of ships in the game, and which are sunk
- the order in which the moves were made
- the locations (cities, railway)

• It's very close to being a QR code; the 'holes' are exactly the right shape and spacing for the alignment marks, and the timing marks are in the right place too. – 2012rcampion Sep 21 '16 at 22:41
• Hmm, I didn't realize that the smallest form doesn't use alignment indicators. – Phlarx Sep 22 '16 at 16:30
• Congratulations, very well done. – Matsmath Sep 22 '16 at 17:58