Puzzle #20
Knife Ridge
12 × 12Expert15 colorsPublished October 8, 2026
Solve it in the solver Download .flow
Colors: Blue, Orange, Green, Red, Purple, Brown, Pink, Gray, Lime, Cyan, Yellow, Vermilion, Sky, Peach, Mint.
Blue is the long color here. It starts beside the top-left corner, runs down the whole left edge, and later winds through the lower middle to reach its dot at row 10, column 9. The upper left packs into neat horizontal bands, but the center stays open for a long time and needs several rounds of thinking ahead.
New to these puzzles? Read how to play first. Connect each pair of dots with a path, fill every cell, and don't let paths cross. This board has exactly one solution.
Hints
Hint 1: where to look
Look at the corners first. The top-left and bottom-right corners each have only two usable neighbors, and so does the cell at row 10, column 12.
Hint 2: the first idea
Blue keeps running straight down the left edge, because each turn right would box in Purple or seal off a small pocket. After that, Orange must run left along the top row to its partner, since dropping down seals off four cells.
Hint 3: the key step
Lime's end at row 5, column 7 has to run right along row 5 to column 10 before it drops to its partner. Any earlier turn down leaves Gray or Blue with no working route a few moves later.
Techniques used: Forced moves, Edges and corners, Dead ends, Bottlenecks, Thinking ahead.
Step-by-step walkthrough
Every step below follows from the rules alone, with no guessing. Try the puzzle first and use the walkthrough when you get stuck.
Step 1 of 19
Three squeezes start things off. The top-left corner has only two usable neighbors, so Blue passes through it and turns down the left edge to row 3. In the bottom-right corner, Mint drops through the corner and runs left to column 10. The cell at row 10, column 12 has only two usable neighbors too, so Peach goes down through it and left to sit beside its partner.
Step 2 of 19
Blue's end at row 3, column 1 could turn right. That would leave Purple boxed in with nowhere to go, so Blue goes down one.
Step 3 of 19
The same choice comes up at row 4, column 1. A turn right would seal off a single cell, so Blue continues down.
Step 4 of 19
At row 5, column 1, turning right would seal off a pocket of two cells. Blue drops once more, to row 6.
Step 5 of 19
Orange's top-row dot could drop to row 2, but that seals off four cells no color can finish. So Orange runs left three along row 1 and drops onto its partner at row 2, column 2. The upper left then fills in as stacked bands. Purple runs down column 2 beside Blue, while Gray, Lime, Pink and Red push right along rows 6, 5, 4 and 3. Green moves right under its other dot, and Blue runs down the edge to row 8 and turns right.
Step 6 of 19
Sky's dot at row 9, column 11 can't go up, because that seals off three cells. Sky goes left one.
Step 7 of 19
Mint's end at row 12, column 10 could climb, but that would seal off a single cell. Mint keeps going left to column 9.
Step 8 of 19
Lime's dot at row 7, column 11 has three choices. Going down seals off three cells and going right seals off one, so Lime goes left.
Step 9 of 19
Green could wander right along the top row, but thinking ahead rules that out. A few forced moves later, Pink's dot at row 3, column 11 would have no move that works. Going up or right cuts Pink off from its partner, and going down boxes in Gray. So Green connects its two ends at once.
Step 10 of 19
Red's dot at row 4, column 12 can't go left, because Red would then be boxed in. Red climbs the right edge to the top row and turns left.
Step 11 of 19
From row 1, column 11, Red can't go down without boxing in Gray, so it keeps going left. That leaves row 2, column 11 with only two usable neighbors, and Pink passes up through it and left along row 2. Red finishes along the top row and drops to meet its other end at row 3, column 8. Pink then runs down column 9 to row 4, and Brown steps down, right and down again toward its partner.
Step 12 of 19
Brown's end at row 5, column 11 could turn left, but that boxes in Lime. So Brown steps right onto its dot and connects. Now row 6, column 12 has only two usable neighbors, and Gray takes it, running down the right edge and back left along row 8 to column 9.
Step 13 of 19
Peach's end at row 10, column 11 could go left, but Blue would then be boxed in. Peach drops onto its partner instead.
Step 14 of 19
Sky faces the same danger at row 9, column 10, since going left boxes in Blue. Sky goes down two and left two along row 11. Blue's lower dot then climbs one and turns left, Mint runs left and up to sit beside its dot at row 11, column 6, and Yellow's lower dot steps left and up. Sky's ends meet at row 10, column 8.
Step 15 of 19
Pink's end at row 4, column 9 can't go down, because that cuts Gray off from its partner. Pink connects with its other end at row 4, column 8.
Step 16 of 19
Lime's end at row 5, column 7 now matters. If it dropped down, a few forced moves later Gray at row 7, column 6 would have no move that works, since going down cuts Gray off and going right cuts Blue off. So Lime goes right one.
Step 17 of 19
The same idea repeats one cell further. Dropping from row 5, column 8 would leave Lime at row 6, column 8 a few moves later with no working move, as every direction cuts Gray off or seals a single cell. So Lime runs right to column 10 and down one.
Step 18 of 19
At row 6, column 10, a turn left would leave Gray's end at row 6, column 6 with no working move, because both of its options cut Blue off from its partner. Lime steps down onto its dot and connects.
Step 19 of 19
Blue's end at row 9, column 8 can't go left, because Yellow's dot at row 8, column 7 would then have no working move. Blue goes up two instead. Gray climbs column 9 and runs left along row 6 to its end. Blue winds left along row 7, down column 6, left along row 9 and down column 4, meeting its other end, which drops down column 2. Cyan, Yellow, Purple, Vermilion and Mint all finish around it.