This puzzle is based on a puzzle found on one of M. Gardner's selections from Sam Loyd's cyclopedia. Rouse Ball attributes the problem to Dudeney, but the reference doesn't match. The correct reference is probably "The Weekly Dispatch 1900.04.29 P324" in Knuth's puzzle list.
The objective is to place as many pieces as you can on a chessboard with at most two pieces on any row, column or diagonal. In the implementation, a "0" represents an empty place and a "1", an occupied place. You may start with an empty board or with some randomly placed pieces (by pressing random) or with some preassigned pieces (by placing them and pressing lock). By pressing anneal, the computer will try to find the maximum by simulated annealing. This takes a few seconds and usually works. By pressing reveal, the computer reveals its solution.
Loyd's puzzle asked for two pieces among the four central squares and seems to imply that his solution is unique, which is not the case. Some solutions (but by no means all) may be found algebraically, as follows. Coordinate the chessboard as (Z/8)2 and consider a set of pairs (x,y) with either y=ax+b or y=cx+d, where a,c are either 2 or 6 and b,d are of opposite parity. We leave it as an execise to show it works. You may also interchange x and y, of course.