Confinia

What is Confinia

Confinia hands you a map with the geography stripped out: a few empty cells joined by dashed lines, and a tray of country tiles beside it. Place every country so that each dashed line joins two nations that genuinely share a land border. Tap a tile, tap a cell, rearrange freely. When the board is full, press Check and every link is stamped green for a real border or red for a false one.

What makes it hard is not knowing where countries sit on a globe, but counting. A cell with five lines leaving it needs a country with at least five land neighbours, which rules out most of the tray at once. Read the board as a shape rather than a map and it turns into a matching problem: the busiest cells demand the busiest countries.

How to play

1. Choose a level, from Easy to Impossible, then tap a tile in the tray and tap an empty cell to place it. Tapping a placed country sends it back.
2. Every dashed line claims that the two countries it joins share a real land border. Sea crossings do not count, and island nations never appear in the tray.
3. Scan is the mid-game test. It checks only the links whose two ends are already filled, so you can validate one corner before committing to the rest. You get four scans on the easy levels and two on Impossible.
4. When every cell is filled, press Check. Green means a true border, red means none. Red links let you keep playing, but the failed check costs stars and points. Once the board is all green the round ends and your score is totalled.

Strategies that work

• Count lines before you count countries. Rank the cells by how many links they have, then hunt for tiles with a matching number of neighbours. Portugal, Denmark and South Korea have exactly one land neighbour, so they only fit a cell with a single line.
• Work outward from forced moves. If only one country in the tray borders two tiles you have already placed, that placement is certain. A chain of forced moves solves most Easy and Medium boards without a single scan.
• Use the first scan early. It is free and costs no star, so fire it once three or four tiles are down and you can still act on the answer. Later scans cost points and a star each.
• Trust the tray. It holds exactly the countries the solution uses, with no spares. If an unlikely nation is sitting there it has a home, and matching it to the cell with the right neighbour count usually collapses the rest.
• Balance speed against certainty. The time bonus decays to zero at the level's limit, ninety seconds on Easy up to five hundred on Impossible, but a failed Check costs more than the seconds you save. A clean win with no hints and no errors extends your streak, worth up to a 1.5 multiplier.

A little history

Confinia is an original game written for this site, but the object it plays with is real and long studied. Treat every country as a point and every shared border as a line between two points and you get what mathematicians call an adjacency graph. That graph underlies the four colour theorem, proved in 1976 by Kenneth Appel and Wolfgang Haken, which says any map drawn on a plane can be coloured with four colours so that no two neighbours match. Confinia reverses the question: instead of colouring a fixed map you receive an abstract diagram and must fit the real border network into it, a task known as subgraph matching. Every board comes from a search that stops only on a working arrangement, so each puzzle has at least one solution.

Frequently asked questions