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How to Solve Zip Number-Path Puzzles
A zip puzzle asks for one thing that sounds simple and turns out delightfully fiddly: draw a single unbroken line that touches every square exactly once while passing through the numbered chips in order - 1, then 2, then 3, and on up. No arithmetic, no timer, no way to lose - just pure route-planning. Once a few habits click into place you stop staring at a blank grid and start seeing the one line hiding inside it. This guide covers the core rule and the techniques that crack almost every board.
The one rule that governs everything
Every zip puzzle rides on a single instruction, and the whole game flows from it:
One continuous line must cover every playable cell exactly once and pass through the numbered chips in climbing order.
Break that sentence into two demands and you have your whole to-do list. First, coverage: the line has to fill the board - leave one square untouched and you are not done. Second, order: reach chip 1, then 2, then 3, and finish on the highest number; out of sequence, a perfectly full board still will not clear. A finished zip is both demands landing on one line that never lifts and never crosses itself.
That "exactly once, never crossing" part is what mathematicians call a Hamiltonian path - but forget the jargon and picture a piece of string laid flat to touch every tile, threaded through the numbers like beads in order.
Start from the fixed numbers
The numbered chips are the only fixed points on the board, so they are where your plan begins. Before you draw anything, let your eye run 1 → 2 → 3 and roughly trace the route between them - not the exact path yet, just which region each leg lives in and where the line has to begin and end.
The two anchors that matter most are the smallest and the largest number: the line must start on chip 1 and finish on the highest chip, fixing the loose ends of your string. Everything between is about covering ground from one number to the next without doubling back.
Playing along? In Mochi Zip you literally cannot start anywhere but chip 1 - tapping any other tile does nothing - a gentle nudge to plan from the numbers outward. The early Berry world hands you tiny 4×4 boards with just a 1 and a 2, so the whole puzzle really is "fill the grid from one number to the other."
Hug the walls and corners
Here is the technique that does the most heavy lifting. The edges of the board - and especially the corners - are the most constrained parts of the puzzle, so they are the easiest to commit to first.
Think about how many ways the line can pass through a tile. An open centre cell has four neighbours; an edge cell has three. A corner has only two - exactly one way through it, in from one side and out the other. A corner is never a decision, just a fact waiting to be written down.
So practise reading the perimeter first. Trace the line around the outside, letting each corner force your hand, and the whole border often resolves before you touch the middle. Then fill the centre inside that frame, where you have room to manoeuvre.
Never strand a corner or a lonely tile
The single most common way a zip route dies is that it walls off a square it can no longer reach. Because every tile must be covered, a cell left with no free neighbour to enter from is a dead puzzle - however beautiful the rest of your line.
Two danger spots to watch. First, corners again: sweep past a corner without entering it and it has only one exit left; spend that exit elsewhere and the corner is orphaned forever. Second, any tile you pass on both sides without entering is quietly sealed off. As you draw, keep asking of every empty square, "can the line still get in here?" The moment the answer is no, back up.
Handy in play: Mochi Zip shows a small cells-covered tally while you draw. If that number stops climbing toward the total, your route has stranded something - retract and rethink.
Mop up between the numbers
When two chips sit far apart, the tempting move is to dash the line straight across. Resist it: a straight rush leaves a clump of untouched cells to one side that you must come back for - except now the line is committed and there may be no way back in.
Instead, treat the trip between two numbers as a chance to sweep - weave through the tiles as you travel, filling the neighbourhood before the next chip. A good zip line rarely takes the shortest path; it takes the one that leaves nothing behind.
The cushion tiles - the sleepy blocks with little closed eyes - change the shape of that sweep. They are walls the line cannot enter, turning a plain rectangle into an irregular room; treat their outline as the border of the space you fill, and hug it like an outer wall.
A simple solving routine
Put it together and you have a loop that clears almost any board:
- Read the numbers 1 → 2 → 3 first and picture the rough route between them, noting where the line starts and finishes.
- Solve the corners - each has only one way through, so draw those forced segments before anything else.
- Work the perimeter inward, letting the edges guide the line, then fill the centre inside that frame.
- Sweep, don't dash, between distant chips - mop up nearby tiles as you travel rather than rushing straight across.
- Check for strays after each stretch: if any empty tile has lost all its entrances, retract and take a different turn.
Retracing costs nothing and the half-drawn line is kept when you lift off, so commit a stretch, check the coverage, peel back the dead-ends, and keep what works.
Common mistakes
- Hitting the chips out of order. Reaching 3 before 2 kills the route - the board can be full and still refuse to clear. Fix the visiting order first.
- Ignoring the corners. Corners have only one path through them; leave them for last and you have often already sealed them off.
- Rushing straight between numbers. The shortest line between two chips is almost never the winning one - it strands the cells it skips.
- Filling the board but ending on the wrong tile. The line has to finish on the highest chip, so plan the finish as carefully as the start.
- Forgetting the cushions are walls. "Cover every cell" means every cell except the sleepy ones - route around them.
Where to go next
The quickest way to make this instinctive is to draw a few lines. Start on the small Berry boards until reading corners and sweeping feels automatic, then let the bigger worlds pile on chips and cushions. Within a handful of puzzles you stop tracing tile by tile and start seeing the whole route click into place - and if you enjoy that "one continuous line" feel, the guides below scratch the same itch.