Logic Masters Deutschland e.V.

My biggest and most difficult project, enjoy! Huge thanks to NPlusOne for thorough testing.

Rules:

• Normal sudoku rules apply.
• The Traveller: The traveller wishes to visit all the planets in the universe. The traveller starts and ends on a planet and must make a path that reaches every planet by moving orthogonally to adjacent cells. The traveller can visit a cell twice but the path must not cross or overlap itself.
• Planets: Diamonds are planets and each planet's digit equals the order in which the traveller visited it. However, two of the planets have not been discovered yet and their locations must be determined.
• Galaxies: Shade some cells where, excluding the centre, each galaxy consists of two orthogonally connected components that are rotationally symmetric around the galaxy centre and do not touch each other. These two components also have the same sum. Galaxies cannot overlap and each galaxy contains one planet. White dots are galaxy centres and their digit is equal to the digit of the planet the galaxy contains. All galaxy centres are given.
• Void: Void cells are not part of a galaxy, and cannot be travelled to. Grey squares are void. All void cells are given.
• Vacuum: Vacuum cells are not part of a galaxy, but must be travelled to. No vacuum cells are given.
• All cells on the grid must either be part of a galaxy, vacuum or void.
• Moons: Black dots are moons and digits on either side of a black dot must be in a 1:2 ratio and belong to the same galaxy. All moons are given.
• Lost In Space: If the traveller enters any cell occupied by a galaxy, they can only leave the galaxy from the centre.
• Toroidal: The grid is toroidal, cells on opposite edges of the grid (e.g. r5c1 and r5c9) are considered orthogonally adjacent. This applies to all previous rules.

Solve Online

Example:

The red line shows the traveller's path, starting at r6c1 and ending at r2c2. Green, purple, and blue shaded cells represent galaxies. Grey squares are void cells and white squares are vacuum cells. Note that r4c3 is visited twice, demonstrating that a cell may be travelled to twice provided the path does not cross or overlap itself.

Puzzle: