node_shift strategy guide
habits that get you closer to optimal, with numbers from the solver that finds each puzzle's best score.
new here? start with the rules.
1. read the chain before you tap
the chain follows an arrow after it has turned. so before tapping, work out where this node will point, then where the next one will. a right turn takes up to right, right to down, down to left, left to up; a left turn goes back the other way.
chains run longer than they look: a random tap reached about 4.9 nodes, and 43% crossed their own trail.
2. the middle travels, the edges aim
a chain that faces off the board ends at once, and since the tapped node keeps its color, nothing changes. so position decides reach:
- the four middle nodes always face a neighbor: 6.9 steps on average.
- edge nodes face outward 1 turn in 4: 4.6 steps.
- corners face outward half the time: 3.3 steps.
turning inward spreads color. turning an edge or corner node outward quietly re-aims just that node.
3. use both turns
flipping the switch costs no move, and 75% of the optimal solutions we sampled mix right and left turns. with right turns only, 73% of colors needed more moves (or more than 5), and the easiest color got harder on 61% of boards. check both turns on every tap.
4. a move can be pure setup
perfect games often include a move that adds none of your color: about half of multi-move optimal solutions do, 41% open with one, and 39% tap a node of a different color than they end on. a setup move re-aims arrows for a later chain. here is a 2-move optimal solution for all yellowoctagons. the first tap (A3, a bluediamond node) swaps a yellowoctagon node for a bluediamond one,the first tap (A3, a bluediamond) turns an yellowoctagon into a bluediamond, but it re-aims A3 and A2 so the second tap can sweep the board.
moves: 0
press to watch the example, or click any node to try it yourself.
rA3 chain: A3 → A2 (points off the board, chain stopspoints off the board, chain stops)
lD3 chain: D3 → D4 → D3 → C3 → C4 → C3 → B3 → A3 → B3 → B2 → A2 → A1 → B1 → B2 → B1 → A1 → A2 → B2 → C2 → B2 → B3 → C3 → C2 → C1 → D1 → D2 (board is all yellow, chain stopsboard is all octagons, chain stops)
5. build toward one big chain
the last move of a perfect game paints the most: a median chain of 11 steps, adding 4.1 nodes of the winning color against 2.7 for earlier taps. so don't judge a move by how much it paints. an early move that leaves the board looking no better is fine if it lines up a long finishing chain.
6. choosing a color
start with the color that has the most nodes: when one color leads, it was among the easiest 82% of the time and the hardest only 4%. but on about one board in five another color is strictly easier, and each is scored on its own, so try all three.
7. habits worth having
- try things. undo and reset are free, and only your best counts.
- check the rotate switch before each tap: it stays where you left it.
- count what's off. a few wrong nodes in a line may fall to one long chain.
- compare with optimal. it's the true minimum, so if you're above it a shorter way exists. a hint shows it one move at a time.
where the numbers come from
measured with node_shift's own engine and exact solver: 20,000 random taps, and 1,000 random boards solved in full (the 764 where every color takes 4 moves or fewer were studied; the right-turns-only check re-solved 150). daily puzzles follow a weekly pattern instead: monday to thursday, one color takes 2 moves and two take 3; friday and saturday, two take 3 and one takes 4 (about one friday in four swaps a 3 for a 1); sunday, one takes 3 and two take 4. nothing needs more than 4, so the advice holds, but expect the numbers to differ.