Space Lanes

Each coefficient has a slider, colour-matched to its term. Move a and the lane's curvature changes. Move c and the whole thing shifts. Somewhere in that space is a set of values where the lane passes through every beacon.

FIT reads out how close you are as a percentage, so you always know whether a change helped. ENGAGE commits, and names any beacon you missed rather than simply refusing. Hazards must be avoided — a lane that touches a mine is not a lane.

It is coordinate geometry with the graph paper taken away and something at stake instead. You will not be asked to solve anything symbolically; you develop a feel for what each coefficient does by watching it happen.