# An Evil Cartesian Psycho

I came up with this puzzle when I was in high school.

There is an island owned by an evil man who keeps some tourists who were visiting the island a few years ago captive.
The authorities demanded him to tell them how many people he has imprisoned and he sent them a letter with a lot of scrambled numbers.
The police cryptographic expert tried to solve the riddle sent by the psycho and did came up with the following chart:

"Obviously you did something wrong with the message!" - said the sheriff to the expert. The expert then stated that he maybe needs some help to crack this one but the message was lost on the police evidence room. All it's left is the list of the points he wrote by hand.

Can you help the cryptographic expert to decode the message sent by the psycho to the police and reveal how many prisoners the psycho keep captive on the island?

Note: The following list is the list of the marked points written by the expert.

(10, 15), (10, 19), (10, 16), (11, 19), (10, 17), (12, 19), (10, 18), (13, 19), (10, 19), (14, 20), (10, 17), (15, 20), (10, 18), (16, 21), (10, 15), (17, 21), (10, 16), (18, 22), (10, 13), (19, 22), (11, 14), (17, 23), (11, 11), (18, 23), (12, 12), (15, 24), (12, 10), (16, 24), (13, 11), (13, 24), (13, 12), (14, 24), (14, 13), (11, 24), (14, 14), (12, 24), (15, 15), (10, 24), (15, 16), (11, 24), (15, 17), (12, 24), (15, 18), (13, 24), (15, 19), (14, 26), (15, 10), (15, 26), (15, 11), (16, 26), (15, 12), (17, 26), (15, 13), (18, 26), (15, 14), (19, 26), (17, 15), (10, 26), (17, 16), (11, 26), (17, 17), (12, 26), (17, 18), (13, 26), (17, 19), (14, 27), (17, 10), (15, 27), (17, 15), (16, 27), (17, 19), (17, 28), (17, 10), (18, 28), (17, 15), (19, 28), (19, 19), (10, 29), (19, 10), (11, 29), (19, 15), (12, 29), (19, 19), (13, 30), (19, 10), (14, 30), (19, 19)

HINT #1:

Maybe writing all the coordinates on a single chain of numbers helps to see the rule... So the $$xs$$ and the $$ys$$ don't mess with your logic.

HINT #2:

Start with collating the $$xs$$...

• You might not want to give this away, but I assume the order of the textual version of the coordinates is important, and it can be solved without the image? Commented Feb 22, 2021 at 17:06
• @LukasRotter, rot(13) Lre, lbh ner evtug. Gur vzntr vf whfg n thvqr gb fbyir gur ceboyrz.
– Pspl
Commented Feb 22, 2021 at 17:10
• In case it helps, rot13(Guvf vf gur ercerfragngvba jvgu crevbq 2 (naq urer'f n TVS bs vg) orpnhfr bs gur boivbhf nfpraqvat cnggrea rirel 2aq pbbeqvangr. Oyhr = Obgu crevbqf unir ivfvgrq vg. Vs gur pbybe vf qnex, fnzr crevbq unf ivfvgrq vg zhygvcyr gvzrf) Commented Feb 23, 2021 at 20:02