This is a mathmatical object I made based off a problem on the /r/puzzles subreddit.

It is a square matrix such that each row's leftmost element times its rightmost element will equal the two inner numbers (in the example below, the top row has 6*7 = 42). Similarly, each column's uppermost element times the column's lowermost element equals the middle digits (in the example, the right column is 7*8 = 56), as read top to bottom.

6 4 2 7
4 2 0 5
8 4 8 6
8 6 4 8

4 x 4 Barron Square

This was then expanded on to be a 8x8 with two digit rows/columns being multiplied to get four digit products

This problem was about creating triangles in a unit circle and determining if the circle's center was enclosed. This was then expanded to a tetrahedron in a unit sphere. Visualizing each randomly generated shape helps verify the logic that determines if the center is enclosed is working correctly.

Results from 2d simulation

The probability that the shapes would enclose the center resulted in surprisingly nice 25% and 12.5%

We used a randomized search that would try to slightly move districts, check continuity and then check the voting results. The method resulted in uniquely shaped maps that optimized each side's winningness.

This problem was about taking a competition where you could choose the number of games at the cost of prize money. It was your job to find the number of games that yielded the maximum expected return.