A map coloring game is a single-player puzzle that gives you a map divided into labeled regions and asks you to fill every region with a color so that any two regions sharing a visible boundary segment end up with different colors. The shared boundary, not the shape or size, defines adjacency, so two regions that merely touch at a single point are not considered neighbors. In the standard formulation, the fewest colors that can properly color any planar map without breaking that rule is called its chromatic number, and the Four Color Theorem states that no planar map ever needs more than four colors. Four Color Map Puzzle is a free browser map coloring game that turns that theorem into five compact, fully auditable levels. Each level is an original planar adjacency graph with labeled regions, visible boundary lines, and a published minimum palette target that an independent exhaustive oracle has verified. Play it with a pointer or with the keyboard, switch between dots, stripes, crosses, and grid patterns instead of relying on hue, and chase a strict total of 1,000 points across the five maps.
What Makes a Map Coloring Game Work
Every map coloring game rests on a small set of rules that turn a picture into a graph problem. A region is one closed area on the map and is drawn with its own letter label. A boundary line drawn between two letters means those regions share an edge segment and therefore count as neighbors. Touching only at a corner does not draw a line, and regions that meet only at a single point are not adjacent. Once you treat each region as a node and each boundary line as an edge, the puzzle becomes a request for a proper coloring of the resulting planar graph: each node gets a color, and every edge must join two different colors.
A second, less obvious rule decides how many colors you need. Four is an upper bound guaranteed by the Four Color Theorem, but a simple chain of four regions only needs two colors, while a triangle needs three. The smallest palette that can properly color a particular map is its chromatic number, and any proper coloring that uses more colors than that still misses the optimization goal. A complete map coloring game therefore has two simultaneous jobs: separate every adjacent pair and hit the minimum.
The Four-Color Theorem and Minimum Palettes
The Four Color Theorem page maintained by Georgia Tech is a primary academic source for both the theorem and the shared-boundary definition. Carnegie Mellon's conflict-graphs course material independently explains the region-to-vertex and border-to-edge translation that turns a picture into a graph, the meaning of a proper coloring, the rule that point-only contact does not count, the fewest-color objective, and the four-color upper bound. Four Color Map Puzzle draws only on the general mathematical framework from these two sources. The five original maps, layouts, names, target palettes, literal solutions, scoring, and interface are original fixtures, and the published minimum targets are not assumed from those displayed literal solutions. An independent exhaustive oracle verifies each one.
That oracle tries every assignment for palette sizes one, two, three, and four in increasing order, enumerating up to all 4^n possible assignments for n regions on that map, and accepts an assignment only when every edge joins two different values. The first feasible palette size is the true chromatic number for that fixed original graph. The test also requires the published literal solution to be proper and to use exactly that minimum. Because the verification is exhaustive rather than heuristic, every target on the score screen is provably optimal for its map.
Five Original Maps in Four Color Map Puzzle
The five fixed levels deliberately progress through different graph structures, so each map teaches a different lesson about minimum palettes. The layouts are drawn without edge crossings, including the central region of the four-region complete graph and the hub of the six-region wheel.
| Map | Regions | Chromatic Number | Structure |
|---|---|---|---|
| River Counties | 4 | 2 | Linear chain, alternating two colors is enough |
| Three Harbors | 3 | 3 | Triangle, every region touches both others |
| Island Ring | 5 | 3 | Odd cycle, cannot alternate with only two colors |
| Capital Districts | 4 | 4 | Planar drawing of the complete graph on four vertices |
| Sunwheel Provinces | 6 | 4 | Hub plus odd five-region rim, rim needs three and hub forces a fourth |
A linear chain needs only two colors because you can alternate them down the line. A triangle forces three because every region touches both of the others, so no two regions can share a color. The odd five-region ring on Island Ring cannot alternate with only two colors, so it bumps up to three. Capital Districts draws the complete graph on four vertices, which is planar in this fixture and demands four distinct colors. Sunwheel Provinces places a hub beside an odd five-region rim; the rim itself needs three colors, and because the hub touches every rim region, it must take a fourth color that none of them uses.
How to Play Four Color Map Puzzle
- Select a labeled region with a click, or with the Left and Up arrow keys for the previous region and Right and Down for the next, then choose one of the four numbered, named, and patterned color buttons.
- Color every region so that the endpoints of every visible shared-boundary line use different colors, while using exactly the disclosed minimum number of colors for that map.
- Choose Check map or press Enter; if the assignment is wrong, repair the first distinct invalid color sequence, then clear all five maps for exactly 1,000 points.
Press X to reset the current map back to an uncolored state. Press R to restart the full run from River Counties with region A selected, every region uncolored, zero score, and no stored mistakes. The same path is covered in the Color the Map Puzzle: Five Levels to 1,000 Points walkthrough if you want a second opinion on scoring strategy.
Accessible Controls Beyond the Mouse
Color choice does not depend on hue. Each palette button shows a number, a plain name, and a pattern: dots, stripes, crosses, or a grid mark. Colored regions continue to display their letter label and pattern, so a player who cannot reliably distinguish two close hues still has two redundant codes for every choice. Every region button is at least 44 pixels in both dimensions and exposes its region, color name, and selected state to assistive technology, which lets screen readers announce the active region and current palette.
| Key | Action |
|---|---|
| Left or Up arrow | Select the previous region |
| Right or Down arrow | Select the next region |
| 1 through 4 | Apply the matching numbered color |
| Enter | Check the current map |
| X | Reset the current map |
| R | Restart the full run |
| Escape twice within the timing window | Replace the puzzle with a spreadsheet-style cover, then twice again to return |
Invalid color numbers, invalid region indices, unknown movement commands, and inputs after completion or deadlock are atomic no-ops, so a stray key never damages the current state. The double-Escape boss key is shared with the GameShell, which means you can swap the puzzle for a neutral cover without closing the tab.
Scoring, Mistakes, and Deadlock
Each verified level awards exactly 200 points, and the five levels therefore total exactly 1,000. An incomplete assignment does not change the score or the mistake history, so you can experiment with partial fills before committing. A fully colored assignment wins only if every adjacent region differs and the number of distinct colors equals the stated minimum. A wrong assignment is recorded by its exact level and color sequence, and rechecking the same unchanged assignment does not add another mistake. The first distinct wrong assignment remains editable. The second different wrong assignment deadlocks the run until you press R to restart. Completion and deadlock freeze selection, coloring, movement, reset, and further checks, which prevents accidental point changes after the run ends.
The best completed score is stored locally when browser storage is available, so the score survives page reloads without sending anything to a server. All coloring, validation, exhaustive fixture testing, scoring, and storage run in the browser. There is no account requirement, no upload, no paid call, no extra package to install, and no server-side puzzle evaluator. Open Four Color Map Puzzle directly and the full 1,000-point route is right there.
If you're weighing options, Learn Fractions Game: Shade Five Equal-Part Targets covers this in detail.