Lab / Kolam Tiles

Slide to a New Kolam

Move tiles through the open cell while preserving a correct square kolam, and watch the orbit invariant.

Technology: React · TypeScript · SVG
Maturity: Beta
Last tested: 2026-07-29

Objective Reach a different correct kolam through legal fifteen-puzzle moves.

Sandbox 02

Slide to a new kolam

How to play: select any highlighted tile beside the open space. The tile moves into that space. Reach a different correct configuration while watching the exact distance indicator.

15-puzzle board

0moves10steps to next configuration

Choose an orbit

$\varepsilon$ value

\varepsilon(X)

+1Invariant under every legal slide

How this value is computed

Read the sixteen entries row by row, counting the empty cell as 0000. If $N$ is the inversion count and the empty cell is at $(a_0,b_0)$ , then $\varepsilon(X)=(-1)^{N+a_0+b_0}$ .

N: 60
$(a_0,b_0)$: (1,1)
Exponent: 62 · even

KolamsFifteen puzzleInvariants

Slide to a New Kolam

Slide to a new kolam

15-puzzle board

$\varepsilon$ value

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15-puzzle board

ε\varepsilonε value

$\varepsilon$ value