# Where am I supposed to be tonight?

We’ve only just met, and you don’t know me from Adam, but I really need your help – it’s a matter of national security.

I work for… well, let’s just say I work for the Government. I’m supposed to be meeting an informant on a beach somewhere in the UK at ten o’clock tonight, but I have totally forgotten where! I wasn’t fully listening when my dispatcher told me where to go, and I’m struggling to interpret the instructions he’s given me. I can’t help but notice you’re doing today’s cryptic crossword over there, so I’m guessing you’re the kind of person who likes a puzzle – please could you help me? I’m desperate…

Instructions:

1. Retrieve ten coloured shapes (act optimally).

2. [Retrieval method]

3. Identify target (population of more than 30,000).

I’m stumped. I mean, how do I do Step 1 - and what does Step 2 even mean?? They’ve also given me this list of ‘tags’ but I don’t know how to apply any of them. Please help!

TASK: Identify the UK town where I am due to meet the informant tonight.

Hint 1:

Ah, I just remembered something - all the shapes in Step 1 of the instructions are quadrilaterals. I wish I could remember more...

Hint 2:

Hold on - I think he said that once you find the right shapes there is a consistent method to working out which colour each individual shape should be assigned...

CSV equivalent available below. Circles coloured using B=Black, R=Red, Y=Yellow; background is Blue.

Y,  R,  Y,  Y,  R,  Y,  Y,  B,  B,  B,  B,  B,
B,  B,  B,  B,  B,  B,  B,  B,  B,  B,  B,  B,
R,  Y,  R,  Y,  Y,  Y,  Y,  R,  Y,  Y,  Y,  R,
Y,  Y,  Y,  R,  R,  R,  R,  Y,  Y,  R,  Y,  Y,
R,  R,  Y,  R,  R,  R,  Y,  R,  R,  R,  Y,  R,
Y,  R,  R,  Y,  R,  Y,  B,  B,  B,  B,  B,  B,
B,  B,  B,  B,  B,  R,  R,  R,  Y,  R,  B,  B,
B,  B,  B,  B,  B,  B,  B,  B,  R,  R,  Y,  R,
B,  B,  B,  B,  B,  B,  B,  Y,  R,  Y,  Y,  R,
Y,  R,  R,  B,  B,  B,  B,  B,  B,  B,  R,  R,
R,  R,  Y,  Y,  R,  B,  R,  R,  Y,  Y,  R,  Y,
Y,  R,  Y,  B,  B,  B,  Y,  R,  R,  R,  Y,  Y,
R,  Y,  Y,  Y,  R,  B,  B,  Y,  Y,  R,  Y,  Y,
R,  B,  B,  B,  B,  B,  B,  R,  Y,  Y,  Y,  R,
B,  B,  B,  B,  B,  Y,  Y,  R,  R,  R,  Y,  B,
B,  B,  B,  B,  B,  B,  Y,  B,  B,  B,  B,  B,
B,  B,  R,  Y,  Y,  Y,  R,  Y,  Y,  R,  Y,  Y,
B,  B,  Y,  R,  R,  R,  Y,  Y,  Y,  R,  R,  R,
B,  B,  B,  B,  B,  B,  R,  R,  Y,  R,  Y,  Y,
B,  B,  B,  B,  B,  R,  R,  B,  B,  B,  B,  B,
B,  B,  B,  B,  B,  R,  Y,  R,  R,  Y,  R,  Y,
B,  B,  B,  B,  B,  B,  B,  B,  B,  B,  R,  R,
B,  B,  B,  B,  B,  B,  B,  R,  Y,  Y,  Y,  R,
Y,  Y,  Y,  R,  B,  B,  B,  B,  B,  B,  B,  B,
R,  R,  R,  Y,  B,  B,  R,  Y,  Y,  R,  Y,  Y,
B,  B,  B,  B,  B,  B,  B,  Y,  Y,  R,  Y,  R,
R,  R,  R,  Y,  B,  B,  B,  B,  B,  B,  B,  B,
Y,  Y,  R,  B,  B,  B,  B,  B,  B,  B,  B,  R,
B,  B,  B,  B,  B,  Y,  R,  Y,  B,  B,  B,  B,
B,  B,  B,  B,  B,  B,  R,  R,  Y,  R,  Y,  B,
B,  B,  B,  Y,  R,  R,  R,  Y,  R,  R,  Y,  R,
B,  B,  Y,  R,  R,  R,  Y,  R,  Y,  Y,  Y,  R,
B,  B,  R,  Y,  R,  Y,  Y,  Y,  B,  B,  B,  B,
B,  B,  B,  B,  B,  B,  Y,  R,  R,  Y,  R,  R,
B,  B,  B,  B,  B,  Y,  R,  Y,  Y,  Y,  R,  Y

• Hm, I think I have an idea for what the second step is (based on the puzzle's presentation and the total number of dots), but I'm not sure how exactly I should be getting the "colored shapes"...
– Deusovi
Jun 29, 2020 at 8:04
• Ah, wait, I see it!
– Deusovi
Jun 29, 2020 at 8:07
• Okay, I've identified ten colors... Not quite sure what to do next. I'll post a partial tomorrow morning if I haven't gotten anywhere (and if I don't forget).
– Deusovi
Jun 29, 2020 at 8:28
• @Deusovi Sounds like you're on the right track! Note that if you have worked out how to perform Step 1, you already know what Step 2's instruction should be... Perform that and see what you end up with... I shall say no more for now! :)
– Stiv
Jun 29, 2020 at 9:08
• I don't think I've fully completed step 1 - I haven't 'acted optimally" yet because there seem to me to be multiple ways to do so. (I do know the general final results of each of those actions, but not yet the specifics of how to act.)
– Deusovi
Jun 29, 2020 at 16:15

At OP's request, consolidating main steps of @Deusovi's solution with my part into a single solution. Personally, I think Deusovi's part was much more challenging than mine, so if you're inclined to upvote, please upvote both.

Summary of Deusovi's work (recommend reading his whole description, which is excellent):

The first instruction suggests breaking the given grid into 10 shapes. The grid is 12 x 35, so it seems natural to split the grid into ten 6 x 7 rectangles. (I actually did have this independently, but all it shows is that I can divide by 10.)

Deusovi's key observation:

Deusovi recognized that these 10 shapes could be interpreted as Connect Four boards during some phase of play. Deusovi was able to "play optimally" each of these grids to determine which player, Red or Yellow, could force a win.

My contribution:

Looking at the winners of the games, I assigned to that rectangle the color of the winner. That yields the picture:

My key observation:

The OP had used the "flags" tag, and indicated in a hint that it had not yet been used. Knowing that the destination was in the UK, I looked at various sources of historical flags. One particularly striking one was composed of only red and yellow, and stuck in my mind. Following the instruction to "Connect Four", I put four copies of this picture together:

Finally:

This is the flag of Northumberland! The only town in Northumberland with more than 30,000 people is where our secret agent should go: Blyth!

• Oh, neat! I absolutely never would've recognized that as a flag.
– Deusovi
Jun 29, 2020 at 18:08
• @Deusovi: two heads are better than one, because I never would've gotten your part! Jun 29, 2020 at 18:14
• So chuffed you worked out what instruction 2 meant and recognised it for what it was! When I stumbled upon it on a list I knew straightaway it was the perfect design for this particular puzzle... Glad you solved it! +1
– Stiv
Jun 29, 2020 at 18:41
• Great puzzle as usual @Stiv! I will admit I backdoor-ed it a bit...saw the tag and looked on a list, and the answer really stood out. Took me a minute to figure out how to connect the dots. Jun 29, 2020 at 18:45
• Now that I've seen this, I don't think I'll easily forget the flag of Northumberland. Jun 30, 2020 at 11:05

# Partial answer - some progress made, not sure how it lines up with instructions

The given grid can be divided into

10 7×6 grids, in a pretty natural way.

These grids share an interesting property: all colored dots are either "pushed up" against the left or the right sides.

These turn out to be

games of Connect Four! If we interpret 'gravity' as going in a certain direction (either left or right), each of these forms a Connect Four game. By counting the colors, we can figure out whose turn it is; then, in each game, there is a player who is certain to win with optimal play.

So... what next?

There is not exactly one optimal play for each player. (In the left-middle board, no matter what yellow does right now, red will win on the next move.)
There is not exactly one winning column for each game. (In the right-middle board, red can win on either column 2 or column 5, depending on yellow's move.)
The piece counts on each board don't seem to spell anything as A1Z26, either in their current state or when the game is played out.

The given instructions (and a hint in the comments) suggest that now is the time to use "Connect Four" as an instruction in some other way. I don't see any natural way to do that though. We likely need to use the winning player colors somehow here, because that's the only real data that both can be extracted uniquely from these games and requires the Connect Four aha. But what to do with that is still unclear to me.

• Fantastic work :) Great job on working out what the image represented and on taking each one to its conclusion - brilliant explanation through that diagram. Sorry you didn't quite spot the next part! It was definitely the most obscure part. I've wanted to do a puzzle using this and then using its name as an instruction for ages. Hopefully people agree it checks out even if it is hard to spot... +1
– Stiv
Jun 29, 2020 at 18:40
• I really love what you did here, and how you recognized it. Glad to have tag-teamed it with you! Jul 1, 2020 at 2:00