What is Simple Coloring?
Simple Coloring is a single-number technique: link every pair of cells where the number has exactly two spots in a row, column or box, then color the chain in two alternating colors. Either every cell of one color holds the number, or every cell of the other does. Any cell outside the chain that sees both colors can’t hold it.
It is also called single-digit coloring or single chains. Skyscrapers and kites are short coloring chains, and coloring lets you follow much longer ones. In Marble Sudoku the number is a marble color, so we use orange and blue rings for the two teams.
Use it in 4 moves
- 1Pick. One number at a time.
- 2Chain. Join every pair of spots that are alone in a row, column or box.
- 3Color. Give the spots two alternating colors along the chain.
- 4Clear. Remove the number from any cell that sees both colors.
Then look for singles where you removed it.
TRY IT · GUIDED EXAMPLE
Color the chain
Only Teal is shown in color. Faded lines join Teal spots that are alone in a row, column or box. Color the chain from the orange spot, then clear the Teal spot that sees both colors.
This is the real board from Marble Sudoku. The nine marble colors stand for the numbers 1 to 9.
- Color
- Teams
- Clear
- Place
Color the chain
Read the example in words
Among other places, Teal has exactly two spots in rows 3, 5, 6 and 8, in columns 5 and 9, and in the center and middle-right boxes. These pairs join eight spots into one chain. Starting from row 3, column 3 as orange, the colors alternate: orange spots are row 3, column 3, row 5, column 9, row 6, column 4 and row 8, column 5; blue spots are row 3, column 9, row 5, column 5, row 6, column 8 and row 8, column 1. Either all orange spots are Teal or all blue ones are. Row 1, column 1 sees an orange spot (same box as row 3, column 3) and a blue spot (same column as row 8, column 1), so it can’t be Teal and is left with a single color: Navy. With numbers turned on, Teal is 4 and Navy is 8.
YOUR TURN · PRACTICE
Color the chains
Each round shows the spots for one color. Find a spot that sees both colors of a chain and tap it. On Easy the chain is already colored. On Hard you color it in your head.
Round color:
Why Simple Coloring works
Each link joins two spots that are the only places for the number in some row, column or box. So exactly one end of every link holds it. If one spot of the chain is true, its partners are false, their partners are true, and so on along the chain.
That leaves only two possibilities for the whole chain: all orange spots true, or all blue spots true. A cell that sees an orange spot and a blue spot clashes with whichever color is true, so it can’t hold the number.
How to color faster
- Start from the two-spot lines. List every row, column and box where the number has exactly two spots. Those are the links.
- Follow one chain at a time. Start anywhere and keep alternating colors as you hop from link to link until the chain ends.
- Look between the colors. The cells to clear sit where an orange spot and a blue spot both have reach, often at the corner of an imaginary rectangle.
- Watch for a clash. If two spots of the same color see each other, that color is false everywhere, and every spot of the other color holds the number.
Simple Coloring vs. Skyscraper vs. X-Wing
| Simple Coloring | Skyscraper | X-Wing | |
|---|---|---|---|
| Built from | Any number of two-spot links | Two two-spot lines | Two two-spot lines |
| Logic | One of two colors is true | One of two tops is true | Both lines use the same two columns |
| Removes | From cells that see both colors | From cells that see both tops | From the rest of both columns |
| Difficulty | Advanced | Advanced | Advanced |
Common mistakes
- Links with three spots. A link needs exactly two spots for the number in its row, column or box. Three spots don’t force anything.
- Mixing two chains. Colors only compare inside one connected chain. Two separate chains need separate color pairs.
- Clearing chain cells. Spots on the chain keep the number. You clear cells outside the chain that see both colors.
- Seeing only one color. A cell must see at least one spot of each color. Seeing two orange spots proves nothing.
Simple Coloring FAQ
What is Simple Coloring in Sudoku?
It is a single-number technique. You link the cells where a number has exactly two spots in a row, column or box, color the chain in two alternating colors, and remove the number from any cell that sees both colors.
Is it the same as single chains or single-digit coloring?
Yes. Simple Coloring, single-digit coloring and single chains are names for the same idea. Multi-coloring is a stronger version that compares two separate chains.
What is a color wrap?
If two spots of the same color see each other, that color can’t be true, because a row, column or box would get the number twice. Then every spot of the other color holds the number.
Is a Skyscraper a kind of coloring?
Yes. A Skyscraper or a 2-String Kite is a coloring chain with just four spots. Coloring finds the same moves and longer ones.
Does this work in Marble Sudoku?
Yes. Pick one marble color, join the holes where it has only two places in a row, column or box, and give them two alternating colors in your head or with notes.
When should I look for it?
When singles, pairs, X-Wings and kites stop finding moves. Coloring is a strong tool for hard and expert puzzles.
PRACTICE IN THE GAME
Color a chain in a real puzzle
When a hard puzzle stalls, pick one color and follow its two-hole links. A cell that sees both teams is often the move that breaks it open.
Next techniqueFinned X-Wing
