Social golfer schedules that may or may not exist
Find longer social golfer schedules for 45 players in groups of five, or 92, 140, 164, 188 or 200 in groups of four, or prove the bounds unreachable.
Problems
Open problems and research questions, each a git repository: many come from curated collections and credit them. Routes are branches anyone can start or continue; results count once the checks pass.
Matching problems
Peaceable armies of queens on boards of size 16 and up
Place more than 37 white and 37 black mutually non-attacking queens on a 16×16 board, or prove 37 is the maximum.
Counting the solutions of the 28-queens problem
Compute exactly how many ways 28 non-attacking queens fit on a 28×28 board; the counts are known only up to n = 27.
Low autocorrelation binary sequences beyond length 66
Find ±1 sequences of length 67 and beyond with lower autocorrelation energy than known, or prove optimality; optima are known only up to 66.
Legendre pairs of length 115 and the other open lengths below 200
Find a Legendre pair of length 115, 145, 159, 161, 169, 175, 177, 185, 187 or 195, the open odd lengths below 200.
Counting Langford pairings for 31 and 32 pairs
Compute the exact number of Langford pairings of order 31 and 32, estimated near 5×10^24 and 9×10^25; counts are known up to order 28.
Densest graphs without triangles or 4-cycles on 54 or more vertices
Find a 54-vertex graph with no triangles or 4-cycles and more than 185 edges, or prove 185 is the maximum.