Four Color Map Puzzle is a color the map puzzle built around five original planar maps whose minimum palettes have been independently verified by an exhaustive oracle. Each map is drawn as a set of labeled regions connected by shared-boundary lines, and your task is to fill every region so that both ends of every line carry different colors. Winning a level means hitting two goals at once: every adjacent pair must differ, and the total number of distinct colors must equal that map's proven minimum. The tool labels every color with a number, a name, and a pattern (dots, stripes, crosses, or a grid mark), so the puzzle never depends on hue alone. Maps that look busy at a glance often have surprisingly small palettes: a four-region chain needs only two colors, while a planar drawing of the complete graph on four vertices genuinely requires four. That gap between the theorem's upper bound and each puzzle's verified minimum is the heart of the game, because it rewards structural reasoning over guesswork.
What Is a Color the Map Puzzle?
A color the map puzzle is a planar graph problem in disguise. You are given a small set of labeled regions on a flat surface, with each pair of regions that share a boundary segment joined by a visible line. The classic version asks whether you can color every region so that no two adjacent regions share a color. The Four Color Theorem, as documented on Georgia Tech's academic page on the Four Color Theorem, answers that four colors are always enough for any planar map, and that fewer can sometimes suffice.
The mathematical quantity for the fewest colors that properly color a given graph is called its chromatic number. A chain of four regions has chromatic number two, because you can alternate colors down the chain. A triangle has chromatic number three, because each region touches both of the others. A complete graph on four vertices drawn in the plane, where every region touches every other, needs four distinct colors. The puzzle's interface makes those relationships explicit: each region is a labeled node, and each shared boundary is a line drawn once from the symmetric adjacency data.
Two regions are adjacent only when they share a real boundary segment. Merely touching at a single point does not count. This follows the standard map-coloring convention also explained in Carnegie Mellon's conflict-graph course material, which converts each region to a vertex and each border to an edge.
How to Color the Map in Five Steps
Use these concrete steps to complete a color the map puzzle level from start to finish.
- Open Four Color Map Puzzle and let it load in your browser; no account, upload, or installation is required.
- Click any labeled region, or move to one with the Left/Right or Up/Down arrow keys. Each region button is at least 44 pixels on each side and exposes its name and selected state to assistive technology.
- Pick one of the four palette buttons (1 through 4). Each choice carries a number, a name, and a pattern, so the color is identifiable without relying on hue.
- Color every region before checking. Incomplete assignments do not change the score or the mistake history when you press Check.
- Press Enter (or click Check map) to submit. If the assignment is proper and uses exactly the level's disclosed minimum, you earn 200 points. If you get a distinct wrong assignment, repair it; a second different wrong assignment deadlocks the run until you press R to restart.
The Five Levels and Their Minimum Palettes
Every level in Four Color Map Puzzle is an original planar adjacency graph, and every minimum target is verified by an independent exhaustive oracle that tries palette sizes one through four and enumerates every possible assignment, up to 4^n combinations for n regions. The first palette size with at least one valid assignment is the true chromatic number. The published literal solutions are also tested to confirm they are proper and use exactly that minimum.
| Level | Layout | Verified minimum palette |
|---|---|---|
| River Counties | Four-region chain | 2 |
| Three Harbors | Triangle, every region touches the other two | 3 |
| Island Ring | Odd five-cycle, alternating with two is impossible | 3 |
| Capital Districts | Planar drawing of the complete graph on four vertices | 4 |
| Sunwheel Provinces | Hub plus odd five-region rim; rim needs three, hub forces a fourth | 4 |
The progression is deliberate. A simple chain teaches the minimum-not-always-four idea, a triangle shows why three colors can be unavoidable, and a planar complete graph demonstrates the genuine four-color case. The chosen layouts avoid edge crossings, including the central region of the four-region complete graph and the hub of the six-region wheel. Adjacency fixtures are structurally checked before gameplay tests: every neighbor index must identify a real region, a region cannot be adjacent to itself, no neighbor can be listed twice, and adjacency must be symmetric so that the visible lines never hide a malformed rule.
Keyboard Controls and Accessibility
The interface is built so that keyboard play is complete, not an afterthought. Left and Up arrow keys move to the previous region; Right and Down move to the next. Number keys 1 through 4 apply the matching labeled color. Enter triggers Check map. X resets only the current map; R restarts the full run from the first level. Invalid color numbers, invalid region indices, unknown movement commands, and inputs sent after completion or deadlock are atomic no-ops, which means they cannot corrupt the run state.
For pointer or touch play, clicking a region selects it and clicking a palette button colors it. Each colored region continues to show its letter and its pattern after selection, so the screen never depends on color recognition alone. Every region and color button exposes its name and selected state to assistive technology. The chosen layouts are drawn without edge crossings, which keeps both pointer targets and visible lines unambiguous for sighted and assistive users alike.
Scoring, Mistakes, and the Boss Key
Each verified level awards exactly 200 points, and five verified levels therefore total exactly 1,000. The best completed score is stored locally in the browser when storage is available; no account, upload, paid call, or server-side evaluator is used. A fully colored assignment wins only when all adjacent regions differ and the number of distinct colors equals the disclosed 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 stays editable; the second distinct wrong assignment deadlocks the run until you press Restart. Completion and deadlock freeze selection, coloring, movement, reset, and further checks, and Restart returns you to River Counties with region A selected, every region uncolored, zero score, and no stored mistakes.
The shared GameShell also provides a double-Escape boss key. Press Escape twice within the timing window to replace the puzzle with a spreadsheet-style cover, and twice again to return. This is the same overlay used by other Lizely keyboard-driven games such as the Fireworks Simulator and the Maze Game, so the muscle memory carries over between tools.
Why Minimum Matters
Four colors are an upper bound from the theorem, not a command to use all four on every map. Using extra colors can separate all neighbors but still misses the optimization goal, because the level's stated target is the fewest-color proper coloring. That is what the verified oracle is checking when it accepts an assignment only when both conditions hold: every adjacent pair differs and the palette size equals the first k for which a valid assignment exists. Aiming for the minimum forces you to reason about cycle parity, hub-and-rim dependencies, and the structure of the complete graph on four vertices, which is the same reasoning used in graph-coloring research and textbook exercises.
If you're weighing options, Fraction Puzzle Game: Shade 5 Cards to 1,000 Points covers this in detail.