I'd like to populate a "tic tac toe" board (grid of 3 x 3 squares) with four appropriate entries at which time a user will attempt to solve. I'm having a hard time coming up with a mathematical solution to creating the four initial entries.
A picture is worth a thousand words so here is a picture of one particular initial setup and solution.
I'm making a web-based game for my kids that encourages them to learn the basics of algebra. The game and source code (Action Script 3) will be available on my action script note page.
I can come up with something that uses brute force to figure out solutions but I'm hoping there is an elegant mathematical solution I can utilize.