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Simple in explanation, the logic of this game forms an unsolved problem in graph theory.

Label the vertices of a simple undirected graph G(V, E) (where |V| = n and |E| = m) with integers from 0 to m. Now label each edge with absolute difference of the labels of its incident vertices. The labeling is said to be graceful if the edges were labeled 1 through m inclusive (with no number repeated).

A graph is called graceful if it has at least one such labeling. The labeling was originally introduced in 1967 by Rosa. The name graceful was later coined by Golomb.

Gracefully labeled graphs serve as models in a wide range of applications including coding theory and communication networking addressing.

The graceful labeling problem is to determine which graphs are graceful.

Despite numerous (more than 200) publications on a graceful labeling over three decades, only very restricted classes includes paths, stars, complete bipartite graphs, prism graphs, wheel graphs, caterpillar graphs, olive trees, and symmetrical trees.

How to play

- Arrange the numbers in auto generated (or custom created) map so that every directly connected numbers will have a unique difference (absolute) value

- Simply drag and drop the numbers in connected circles to arrange the numbers to satisfy the conditions stated above

Calming and relaxing experience while playing to help you focus. So just focus and even the hardest level could be solved with logic and deduction reasoning.