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Numbers Hexagonal Board Also Known as Hamiltonian path

Terminus Hive

Draw one line through every district of a hexagonal map, calling at the numbered stations in order and finishing on the last. Every district touches up to six others.

  • Four levels: Easy to Extra Hard
  • 3 techniques on its ladder
Terminus Hive on iPad: a board in progress
Terminus Hive on iPhone: a board in progress
About the Game

How Terminus Hive Works

Dr. Hex, who explains the hints on the hexagon games

The rules are Terminus's: one line from station 1, one district at a time into a neighbour it has not used, calling at the numbered stations in order, never through a closed crossing, and finishing on the last station once everything else is served.

What changes is the map. The districts are hexagons, so each one touches up to six others where a square touches four, and every row sits half a step along from the next, so there are no columns to plan down. More neighbours means more ways to go, and more ways to leave a district behind that nothing can reach later.

The map is 19 districts on Easy and Medium and 37 on Hard and Extra Hard. Tap a neighbour or drag your finger through; a drag only enters a district once your finger is well inside it, so clipping a corner does not step into a third one. Terminus Hive is played from Practice and is not part of the daily set.

The Rules

  1. 1

    One Line, Every District

    Start at station 1 and extend the line one district at a time into a neighbour it has not used, until every district is served. Tap a neighbour or drag your finger through.

  2. 2

    Stations in Order

    Call at the numbered stations in order, 1, then 2, then 3, and only arrive at the last one once every other district is served.

  3. 3

    Six Exits

    A district touches up to six others, not four. A district that touches many is easy to strand: pass it too early and nothing can reach it later.

  4. 4

    Closed Crossings

    A thick bar between two districts is a crossing the line cannot pass. Route around it.

  5. 5

    A Wrong Route Costs a Heart

    Every map has exactly one route that serves every district. If your line has left it when it reaches the next station, or when it has nowhere left to go, that costs a heart. Carrying on costs nothing more until you back up onto the right route. A step the map does not allow is refused for free, and backing up is always free. You have three hearts a board.

On iPhone and iPad

The real screens.

Every picture on this page is the app itself, on a board from the game.

Terminus Hive on iPhone: a hint card teaching Only Way Out, with the squares it uses lit on the board
A hint teaching Only Way Out
Terminus Hive on iPad: a hint card teaching Only Way Out, with the squares it uses lit on the board
A hint teaching Only Way Out
History

Where Terminus Hive Comes From

Puzzles where one route visits every cell are usually set on a square grid, where you can plan along a row and down a column. Terminus Hive is Dayzle's Terminus moved onto a hexagon, built in September 2026. The rules, the hints and the way a wrong route is judged are Terminus's; the map is new.

The board stops at 37 districts. On the next size up, pinning the map to a single route took closing 41% of its crossings, and the boards measured no harder than the 37-district ones.

Four Levels

How the Levels Differ

Easy and Medium are a small hexagon of 19 districts, with about 9 and about 8 stations. Hard and Extra Hard are a bigger hexagon of 37, with about 12 and about 11 stations. Hard has more closed crossings to route around; Extra Hard has long runs between stations where a corner is easy to cut off.

Size does not tell Easy from Medium, or Hard from Extra Hard. Each board is built first and then measured the way a Terminus board is: the game walks its route and counts the real choices left at each step once every move that would strand a district or cut off the next station is ruled out. The count decides which of its size's two difficulties the board goes into, on the same scale as square Terminus.

The Technique Ladder

3 techniques, easiest first.

In Dayzle the hint and the solver are one engine, so these are the steps it takes to solve a Terminus Hive board, from the first you'll meet to the rarest. Open one for a worked example and a clip of the hint teaching it on a real board.

Terminus Hive has no graded technique ladder. From the start of a board the three rules above settle about a quarter of the route before a real choice comes up, and at those points a hint says plainly that no rule it knows forces the next district and shows one taken from the route that finishes. A harder board is one with more of those real choices; six neighbours per district make each choice wider, which is why the hexagon is smaller than the square Terminus map at every difficulty.

Only Way Out Beginner Every district beside the end of the line but one is already served, closed off, off the map, or a station whose turn has not come.

Look at the up to six districts touching the end of your line. Cross off the ones already served, the ones behind a closed crossing, and any station whose turn has not come. If one is left, the route goes there.

Dr. Hex, who explains the hints on the hexagon games
Terminus Hive: the hint teaching Only Way Out on a real board. Every district beside the end of the line but one is already served, closed off, off the map, or a station whose turn has not come.
The app's own hint, on a board from the game.
Stranded District Basic A step that would leave some unserved district with no way in and out.

The line has to get into every district and out again, so an unserved district needs at least two open neighbours (the last station needs only one). Take each district you could step to in turn, picture the line going there, and look at the districts you would be turning your back on.

Say the line runs past a corner of the map, where a district touches only three others. If the step you are about to take would leave that district with one open neighbour, the line could reach it but never leave, so that step is a trap.

Dr. Hex, who explains the hints on the hexagon games
Terminus Hive: the hint teaching Stranded District on a real board. A step that would leave some unserved district with no way in and out.
The app's own hint, on a board from the game.
Cut Off Intermediate A step that would leave the line unable to reach the next station, or the districts it has to serve on the way.

When more than one step is still safe after checking for stranded districts, look at the next station. From each district you could step to, can the route still reach that station, and every district it has to serve before it? Step to the one that can.

Dr. Hex, who explains the hints on the hexagon games
Terminus Hive: the hint teaching Cut Off on a real board. A step that would leave the line unable to reach the next station, or the districts it has to serve on the way.
The app's own hint, on a board from the game.
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