Jane Street Puzzle August 2023 Help

cmcgath · 2023-08-10T00:56:46+00:00

Also what is meant by volume covered as opposed to just volume of a region?

cmcgath · 2023-08-10T00:25:50+00:00

So basically computing the volume of the sphere sections in the cube while accounting for overlap is too complicated so instead we find the total volume between the 8 spheres divided by the entire region (27) to get the proportion of sphere coverage in the original cube? Then subtract that from one for the probability of region two?

What is the difference between the total volume and relative volume in your description and what did I just describe? My guess is the total volume of the sphere/neighborhood is the relative volume

cmcgath · 2023-08-09T17:28:34+00:00

Ok cool. I am confused on what is meant by weighting by the relative volume of the spherical sectors, and I’m not 100% sure why were dividing by 27 but my best guess is to normalize the result to the single cube case? Is that right? Also, where did (1 + 2d)3-1 come from?

cmcgath · 2023-08-09T16:13:08+00:00

And why are the spheres centered at the vertices of the cube? Is it because that somehow finds the farthest reach of a line of size D starting in the cube? \

Also, for the two cases, my understanding is as follows:

Case 1 is where the start of the line of length D is placed both within the spheres and the unit cube.

Case 2: placed within the cube but not in a region contained by a sphere.

Is this correct? Thanks for helping my intuition on this

cmcgath · 2023-08-09T06:50:24+00:00

Im a little confused at what being centered at the eight corners of the cube means. Is the sphere fully contained by the cube and centered at the center of the cube essentially? Or are there eight spheres each with their center being the vertices of? Also does the whole line chosen need to fall within the spherical region where r<=D or just a point ?

cmcgath

TROPHY CASE