Twelve plants sit on a garden-shop bench, plotted by the sun they want and the water they drink. Three markers — the gold ×'s — start somewhere on the bench, and from there the whole method is two moves you make yourself: every plant claims the × it is nearest to, then every × walks to the balance point of the plants that claimed it. Do it again. And again. The page marks each half-step right or wrong and tells you what to look at, never what the answer is. Two things are worth finding out: it always stops, and where it stops depends on where you started it.
The method never says where to begin — that part is a guess, and it is yours. Pick one of the four guesses below and press Begin the loop. When a run finishes, come back and pick a different one: the interesting question is whether the plants end up grouped the same way.
starting layout
A pass is two half-steps and you do both. Claim: every plant goes to the × it is nearest to — all twelve, every pass, because a plant can change hands when the ×'s move. Move: each × walks to the balance point of the plants that claimed it — average their sun, average their water. Press Check my work at the end of each half-step; it will not let a wrong half-step through, and it will not tell you the answer either. Keep going until a pass asks nothing of you: that is the loop stopping, and it always does.
1, 2 or 3 (0 takes the claim
back). Move an ×: drag it, or Tab to it and use the arrow keys — one press is half a step of the
grid, Shift is four. Marks: × 1 → gold filled ○ · × 2 → ink open
□ · × 3 → ink filled △ (shape and fill, never colour alone). An
unclaimed plant is a small hollow dot. A dashed ring means "that one is wrong"; a gold halo means
"that one is right".A balance point is an average and nothing else: add up the group's sun hours and divide by how many plants are in the group, then do the same with the cups of water. That is all "move each × to the middle of its plants" means. While a run is going this panel shows a worked example on numbers that are not on the bench, so it can teach the arithmetic without handing you an answer; once a run has converged it shows that run's own sums.
Every run you finish is written down here — which start it came from, how many passes it took, and how big the three groups ended up. Finish two runs from different starts before you decide what this bench "really" looks like.