Yin-Yang
Balance black and white on the grid
Yin-Yang is a two-coloring logic puzzle with a beautifully balanced constraint set. Fill every cell with either a black or white circle. Both black cells and white cells must each form a single connected group (reachable through orthogonal moves). Additionally, no 2x2 square can be entirely one color. Some cells are pre-filled as starting clues. The dual connectivity requirement creates an elegant tension — expanding one color to stay connected can threaten to disconnect the other.
How to Play Yin-Yang
Two Colors
Every cell must contain either a black or white circle. No empty cells in the solution.
Black Connectivity
All black cells must form one connected group. You can reach any black cell from any other through adjacent black cells.
White Connectivity
All white cells must also form one connected group. The same connectivity rule applies.
No 2x2 Blocks
No 2x2 square of cells can be entirely black or entirely white. This forces the colors to interweave.
Given Circles
Some cells start pre-filled with black or white circles as anchor points for your deductions.
Balance Required
The dual connectivity constraints mean neither color can be pushed into thin, fragile corridors without risking disconnection.
Strategy & Solving Tips
Yin-Yang solving requires simultaneous attention to both colors' connectivity. These techniques help maintain the balance.
- If coloring a cell would disconnect either color, it must be the opposite color
- The 2x2 rule is easiest to check: if three cells of a 2x2 square share a color, the fourth must be different
- Work from given circles outward, extending connected paths for each color
- Thin "bridges" of one color (single-cell-wide connections) are fragile — they often force nearby cells to maintain connectivity
- Corner and edge cells have fewer neighbors, making connectivity easier to analyze there
- If two same-colored cells can only connect through a specific cell, that cell must be the same color
Yin-Yang FAQ
Does "connected" include diagonal connections?
No. Connectivity is only through orthogonal (up/down/left/right) adjacency. Diagonal neighbors don't count for connection purposes.
Are there always equal numbers of black and white cells?
Not necessarily. The puzzle requires both colors to be connected and obey the 2x2 rule, but the counts don't need to be equal.
What if I place a cell and can't tell if it breaks connectivity?
Try tracing a path from any cell of that color to every other cell of that color. If you can't reach one, connectivity is broken. Focus on areas where the color forms narrow passages.
Why is it called Yin-Yang?
The name references the Chinese concept of complementary forces — black and white, intertwined yet distinct. The puzzle embodies this perfectly: both colors must coexist, connected and balanced, each constrained by the other.
Ready to Play Yin-Yang?
Find the balance in Yin-Yang — the two-color puzzle where black and white must both stay connected while neither overwhelms the other. Simple rules, deep harmony.