The Four Color Map Puzzle for beginners is a five-level browser game in which you color every labeled region so that regions joined by a visible boundary line receive different colors, and each completed map uses exactly its proven minimum number of colors. That last condition matters: the Four Color Theorem guarantees that four colors are enough for a planar map, but it does not mean every map should use all four. The available palette has four numbered, named, patterned choices, while each level displays its own required minimum. A visible line is the adjacency rule: regions sharing a boundary segment must differ, but regions that merely meet at one point do not count as adjacent. Every region must be filled before a completed assignment can be judged. You can select a region and color with a pointer, or move between regions with the arrow keys and apply colors with number keys 1–4. Press Enter to check. Each verified map is worth exactly 200 points, with 1,000 points available across the run. The challenge is finding the minimum palette while keeping every shared boundary valid.
Four colors are a ceiling, not a quota
Georgia Tech’s Four Color Theorem overview presents the central result in map-coloring terms: no more than four colors are needed for regions of a planar map when regions sharing a boundary must have different colors. Carnegie Mellon’s conflict-graphs course material explains the useful graph translation: each region becomes a vertex, each counted border becomes an edge, and a valid assignment is a proper coloring. The fewest colors that can produce that coloring is the graph’s chromatic number.
This distinction gives beginners two separate goals. First, the ends of every visible line must have different colors. Second, the number of distinct colors must equal the level’s stated minimum. Four colors may separate all neighbors and still miss the optimization goal. Conversely, using only two colors on an odd ring cannot work because a two-color alternation cannot close around the ring.
| Map | Structure to inspect | Proven minimum |
|---|---|---|
| River Counties | Four-region chain | 2 colors |
| Three Harbors | Triangle in which every region touches both others | 3 colors |
| Island Ring | Odd five-region cycle | 3 colors |
| Capital Districts | Complete graph on four regions | 4 colors |
| Sunwheel Provinces | Odd five-region rim with an adjacent hub | 4 colors |
The targets are not inferred from a single sample coloring. An independent exhaustive oracle tests every assignment for one, two, three, and four colors in increasing order. The first palette size with a valid assignment becomes the true minimum, and each published literal solution must also be proper and use exactly that minimum. For a proof-focused explanation of that audit, see how the minimum color targets are verified.
Choose regions and colors with either control method
The pointer route is direct: select a labeled region, then select one of the four color buttons. Each color choice includes a number, a name, and a symbol: dots, stripes, crosses, or a grid mark. Colored regions continue to show their letter and pattern, so the puzzle does not rely on hue alone. Every region button is at least 44 by 44 pixels and exposes its region, color name, and selected state to assistive technology.
| Task | Pointer route | Keyboard route |
|---|---|---|
| Select a region | Click the labeled region | Left or Up selects the previous region; Right or Down selects the next |
| Apply a color | Click a numbered palette button | Press 1 through 4 |
| Check the assignment | Choose Check map | Press Enter |
Press X to reset the current map and R to restart the entire run. Invalid color numbers, invalid region indices, unknown movement commands, and inputs after completion or deadlock are atomic no-ops: they do not advance the puzzle or alter its state. This makes it safe to experiment with keyboard commands while learning the interface.
How to complete a map in Four Color Map Puzzle
- Open the Four Color Map Puzzle and read the level name and its displayed minimum-color target. River Counties begins the run with a two-color target.
- Select the first region you want to color. With a pointer, click its labeled area; with the keyboard, use Left, Up, Right, or Down until the intended region is selected.
- Apply a color by clicking a palette button or pressing its matching number from 1 through 4. The button’s number, name, and symbol provide three ways to identify the choice.
- Follow the visible boundary lines from the selected region. Every region connected to it by a line must receive a different color. Ignore regions that only meet at a single point.
- Keep track of the number of distinct colors in use. A valid palette cannot exceed four, but it must also match the level’s disclosed minimum exactly.
- Fill every labeled region before checking. An incomplete assignment cannot be judged as a completed solution.
- Choose Check map or press Enter. The assignment wins only if every adjacent pair differs and the number of distinct colors equals the stated minimum.
- If the check identifies an invalid assignment, repair that first distinct invalid assignment and check again. Do not count point-only contacts as conflicts or add unnecessary colors merely because four are available.
- Continue through the five fixed maps. Each verified level adds exactly 200 points, allowing a completely correct run to reach the full 1,000-point total.
A beginner plan for the five maps
Each level’s graph structure gives you a practical starting point without needing a printed answer key:
- River Counties: The four regions form a chain. Alternate the two target colors from one end to the other, checking each new region against the previous one.
- Three Harbors: All three regions are mutually adjacent. Each therefore needs its own color, which explains the three-color minimum.
- Island Ring: The five regions form an odd cycle. Two alternating colors cannot close it, so introduce a third color to resolve the unavoidable odd-cycle conflict.
- Capital Districts: Every pair of the four regions shares an adjacency. All four must receive distinct colors, matching the four-color target.
- Sunwheel Provinces: The five-region rim needs three colors because it is an odd cycle. The hub touches every rim region, so it cannot reuse any of those three colors and requires the fourth.
Use the region letters to track your reasoning, and revisit every visible line after the last region is filled. A map can look balanced by eye while still containing a conflict between two distant regions, but the explicit line graph makes that check direct.
How mistakes affect the run
An incomplete assignment does not change the score or mistake history. A fully colored assignment wins only when all adjacent regions differ and the number of distinct colors equals the stated minimum. This means there is no partial credit for a partially colored map and no penalty for checking one before every region is filled.
A wrong assignment is recorded by its exact level and color sequence. Rechecking the unchanged assignment does not add another mistake. The first distinct wrong assignment remains editable, but submitting a second different wrong assignment deadlocks the run until Restart. This makes the order of checking important: once a solution has been checked and found wrong, correct the existing assignment rather than making a separate experimental change.
Each verified level awards exactly 200 points. The complete scoring route is 5 maps × 200 points = 1,000 points. Completion and deadlock both freeze selection, coloring, movement, reset, and further checks. Restart returns to River Counties with region A selected, every region uncolored, zero score, and no stored mistakes. The best completed score is stored locally when browser storage is available.
Browser play and accessibility
Coloring, validation, exhaustive fixture testing, scoring, and storage all run in the browser. There is no account requirement, upload, paid call, new package, or server-side puzzle evaluator. The five original maps also expose several distinct graph structures, so beginners can compare a chain, triangle, odd cycle, complete graph, and hub-and-rim arrangement instead of solving five variations of the same coloring rule.
The shared interface includes a boss key. Press Escape twice within its timing window to replace the puzzle with a spreadsheet-style cover, then press Escape twice again to return. The accessible numbered, named, patterned palette and complete keyboard controls also mean that region selection, color application, checking, reset, and restart do not depend on precise pointing or color perception alone.
Run this check before submitting
Use the following checklist each time you finish coloring a map:
- Every labeled region contains a color.
- Both ends of every visible shared-boundary line use different colors.
- Regions that only touch at a point have not been treated as adjacent.
- The number of distinct colors equals the map’s displayed minimum, not merely the largest available palette.
If all four checks pass, choose Check map or press Enter. The intended beginner routine is straightforward: read the line graph, keep neighbors different, count the palette, fill every region, and then let the game validate the complete assignment against both the adjacency rule and the exact minimum.
Related reading: Fraction Shape Puzzle for Beginners: Controls and Checks.