In the image below, there are two sets of points, green and red. One of them is "random" while another one has been produced by me via clicking points into the square. Market resolves to YES if the green one has been produced by me and NO otherwise.

One of the point sets has been produced by sampling from a uniform distribution over a square. The length of this square is 

 than the bounding box in the square above. Call this the Hidden Square. I won't tell you the side length of the Hidden Square.

Another of these point sets has been produced by sampling from me. Some details of the data generation process:

To elaborate on the last point, here is a hypothetical example of such a transformation: "Given a point, round its x-coordinate to the nearest multiple of 10, and then add a uniformly random integer between 0-9 to it." Intuitively, this makes the set of points "more random", i.e. harder to distinguish from the "actually random set".

I won't tell which transformations I've used.

EDIT: Here are the transformations I used:

The length of the hidden square is 400 - 6*2, with the same center as the bounding box.

Here is a market on how many points it will take for traders to figure out the answer: 

https://manifold.markets/Loppukilpailija/how-many-points-are-needed-to-disti-74e061c28bb6

The data in a more convenient form. The bounding box in the image has corners at (100, 100) and (500, 500).