# Density™ 3 - The Game!

The last Density™ puzzle (here: Density™ finally back from holiday!) proved that OP plays too many games, so we went ahead and created a game of our own!

If you'd like to create your own Density™ puzzle, the rules are as follows:

1. The resolution of the grid is 72x72 squares
2. No words, text, numbers or symbols can be used
3. The tags should indicate what types of solving strategies are required
4. You must specify the number of words + letters in the final answer

# Density Puzzle #3

Where is our fictional game taking place?

I think this is

Auckland Harbour Bridge

at

(-36.83, 174.75)

and the (8,3,7) solution is

AUCKLAND NEW ZEALAND.

You can see

the bridge and its immediate environs in the circle at top right, and (in a rather different view) in the large image -- though I'm not sure what view would show you the curve in the southern road without also showing the protruding jetty/pier/whatever-it-is that's visible in the inset. Maybe it's a post-apocalyptic game set in a future where that jetty/pier/whatever is underwater? [OP clarifies that this is just a minor inaccuracy in drawing and not significant.]

The 3x3 grids are

digits, as follows:

... 0    #.. 1    #.. 2    ##. 3    ... 4
...      ...      #..      #..      ...
...      ...      ...      ...      #..

#.. 5    #.. 6    ##. 7    ... 8    #.. 9
...      #..      #..      ...      ...
#..      #..      #..      ##.      ##.

which we may explain

by supposing that cells in the first two rows count 1 and cells in the bottom row count 4, but as we'll see that's not exactly the right rule.

The grids at top right

give northings and eastings; the northings are red because they are negative, New Zealand being in the southern hemisphere [citation needed].

Now, what about the 3x3 blocks at top left?

It seems likely that they say PSE somehow. The third is a 5, strongly suggesting A1Z26, and I think the intended rule is that the scoring goes as follows:

114
144
444
.

Then

the blocks indicate the numbers 16, 19, 5, which is exactly what we need to make PSE. (Note: in the original version of the puzzle there was a minor error that made this not quite work, but it's been fixed now.)

The bars at top left

look like they measure 12, 11, 4 pixels respectively. Again A1Z26 yields nothing useful (LKD) and if there's useful information here I'm failing to see what it is. [OP clarifies in comments that they're just window-dressing.]

• I'm pretty sure that there are 6 cells worth 4 in the grids which are filled starting from the bottom row and going up. This means your initial thought of the letters at top left were right and gives 27 numbers to work with to cover all of the alphabet – user39583 Dec 17 '20 at 2:27
• Looking at it again, that wouldn't work for the middle letter, so maybe it's something else after all. – user39583 Dec 17 '20 at 2:31
• Nicely done! I've deliberated with the community as to how we tie up the loose ends, so I'll leave a comment below for you and then perhaps you might want to edit your answer? – Dmihawk Dec 17 '20 at 3:20
• Should also be noted that the answer is the hometown of OP :D – Dmihawk Dec 17 '20 at 3:24
• I see the puzzle image has had the slip-up fixed; I've amended my answer accordingly. – Gareth McCaughan Dec 17 '20 at 20:05

Gareth McCaughan is 100% correct, but I made a mistake on the original post of the question - to clarify the number system, my notes from making the puzzle are below

These represent the numbers from 1 - 26 (left to right, top to bottom)
In the Density:
- Symbols in black are positive numbers
- Symbols in red are negative numbers
- Symbols in white are A1Z26 encoded letters

The symbols below the "planet" correspond to coordinates in the real world. I haven't found the pattern to generate all the digits, but given the ones at the bottom (the "inventory" to call it some way), it'd need to have a structure like:

N3a.b3, E1cd.ce

Considering possible coordinates, I'd say it is somewhere in Japan, probably inside or near Tokyo (whose approximate coords are 35.690, 139.690)

• This is a very partial answer, with literally no confirmed progress, and would've been better off as a comment. Please don't post partials without some significant progress. – bobble Dec 16 '20 at 23:57
• Can you also explain the structure? I've never seen that kind of notation before (at first reading I thought it was chess) – Dmihawk Dec 16 '20 at 23:59
• I am not convinced that the digits you think are 3s are actually 3s. (I agree that they are numbers and that they are probably coordinates.) My reason for being unconvinced is that I suspect the ones at top left are 16, 19, 5 signifying P,S,E, which to me suggests some sort of additive thing where each of the 3x3 cells has a value, and that three-on-the-left will be worth strictly more than 5. – Gareth McCaughan Dec 17 '20 at 1:24
• Er, actually it's not three-on-the-left that you're saying makes 3, so I'm not sure how much evidence against your 3s that is even if I'm right about PSE. But I'm not sure what evidence for the 3s there is; is there any reason why the numbers at the bottom should be 1,2,3? – Gareth McCaughan Dec 17 '20 at 1:26
• The different colours of the northings and eastings (if that's what they are) at top right suggests to me that one (probably the red one) is negative, which would put this in the southern hemisphere. – Gareth McCaughan Dec 17 '20 at 1:27