node_shift strategy guide
practical tips for getting closer to optimal, with numbers from the same solver that computes each puzzle's optimal scores.
new to the game? start with the rules. the short version: a click turns a node, then a chain follows the new arrows and paints every node it visits with the clicked node's color.
1. trace the chain before you click
the chain always follows a node's arrow after it turns, never before. so for any click, ask: where will this arrow point once it turns, and where does the next node point once it turns? a clockwise turn sends up to right, right to down, down to left, and left to up. counter-clockwise goes the other way.
chains are often much longer than they look. in our tests a random click on a random board visited about 4.9 nodes on average, and about 43% of chains passed through some node more than once.
2. middle nodes travel, edge nodes aim
where a node sits decides how far its chain can go. a click whose new arrow points off the board stops immediately: only that node turns, and since the clicked node keeps its color, nothing changes color at all.
- the four middle nodes always point at a neighbor, so their chains always continue. average chain: 6.9 steps.
- edge nodes point off the board after 1 in 4 turns. average chain: 4.6 steps.
- corner nodes point off the board after half of all turns. average chain: 3.3 steps.
that makes clicks that turn inward the ones that spread color, and clicks that turn an edge or corner node to face outward a cheap way to re-aim a single node without disturbing anything else. both are useful; just know which one you are making.
3. use both directions
switching direction is free, and the best solutions lean on it. of the optimal solutions we sampled, 75% mixed clockwise and counter-clockwise clicks. when we re-solved boards with clockwise turns only, 73% of colors needed more clicks (or could not be done within 5), and the puzzle's easiest color got harder on 61% of boards.
before every click, check both turns: the same node turned the other way often starts a completely different chain.
4. setup clicks are not wasted clicks
it is tempting to only make clicks that add your target color. perfect games often don't. in our sample:
- about half of optimal multi-click solutions included a click that added no nodes of the target color at all;
- 41% started with one; and
- 39% clicked a node of a different color than the one they finished in.
a setup click turns arrows so that the next chain runs where you need it. here is a real 2-click optimal solution for all white. the first click (A3, a blue node) actually turns a white node blue. it doesn't matter: it re-aims A3 and A2, and the second click starts a chain that sweeps the whole board.
clicks: 0
press ▶ to watch the example, or click any node to try it yourself.
rA3 chain: A3 → A2 (points 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 white, chain stops)
5. plan the finishing click first
the last click of a perfect game does most of the painting. in the optimal solutions we sampled, the final chain was a median of 11 steps long and added 4.1 nodes of the winning color on average, against 2.7 for every earlier click.
so work backwards. look for a node of your target color whose chain would already run through most of the board, find where it breaks off (an arrow that turns off the edge, or a loop that misses a corner), and spend your earlier clicks fixing just those spots.
6. pick your color, then try the others
a good first guess is the color that already covers the most nodes: when one color starts with more nodes than either other, it was tied for the easiest color 82% of the time, and the hardest only 4% of the time. but on about one board in five another color is strictly easier, and all three colors are scored separately, so it pays to play each one.
7. good habits
- explore with undo. undo takes back a click and its count, so a promising-but-wrong line costs you nothing. (turn on hard_mode when you want no safety net.)
- watch the switch. the turn direction stays where you left it from one click to the next, so check it before every click.
- count what's left. if only a few nodes are off-color and they sit on one line, a single long chain can often catch them all.
- chase optimal. each puzzle's optimal score per color is the true minimum, computed by an exhaustive search, so if you are above it there is a shorter way.
about these numbers
the figures above come from experiments with node_shift's own rules engine and exact solver: 20,000 random clicks on random boards, plus 1,000 random boards solved exhaustively, of which the 764 where every color can be finished in 4 clicks or fewer were analyzed (one optimal solution per color). the clockwise-only comparison re-solved 150 of those boards. daily puzzles are not a uniform sample of random boards: they are picked for a mix of difficulties (by the fewest clicks for the puzzle's easiest color, about 2% 1-click, 38% 2-click, 45% 3-click, and 15% 4-click), and each week is ordered from the easiest puzzle on monday to the hardest on sunday. the tips hold the same way, but expect the exact numbers to differ, and individual puzzles to vary.