Jane Street Interview Question: If you extend the faces of a ... | Glassdoor.co.uk

# If you extend the faces of a tetrahedron as planes

infinitely in all directions, how many regions does this divide 3D space into?

4

15

Interview Candidate on 19 Dec 2012
0

There is 4 planes. You are either left or right of each so you could be in one of 2^4 = 16 distinct regions.

kt on 26 Feb 2013
1

Did they specified if the subspaces had to be disjoint?

Bogdan on 8 Apr 2013
3

Think of the tetrahedron as the edge of a cube. Think of extending the planes as extending the cube into a 2x2x2 cube. Think of the bottom of the tetrahedron as a plane slicing 7 of the 8 cubes (except for the one in the opposite corner). So 7x2 + 1 = 15.

Anonymous on 23 Jul 2013
1

You might be able to visualise this, I think it helps. There will be one region for each vertex, edge and face and one region inside the tetrahedron. So there will be 4 + 4 + 6 + 1 = 15 regions.

Barry on 2 Dec 2014
0

Use Barycentric coordinates, observe that if the coordinates are w, x, y, z then w + x + y + z = 1. Lying on a side of a plane is given by the variable being positive, and observe that other than all variables being negative, all other combinations are possible.

Bary_Basher on 14 Aug 2018