Logic Masters Deutschland e.V.

Normal sudoku rules apply. Digits along a thermometer must increase from the bulb end and do not need to be consecutive.

The grid is further separated into 4 concentric rings as indicated by the dotted lines. These rings form the orbits of various comets circling a black hole in the grid’s central cell. Comets are represented as thermometers with the bulb end being the head of the comet. All comets must be positioned such that they appear to be orbiting the black hole in a clockwise direction of rotation (i.e. always making right turns at the corners). Comets placed in an orbit must stay within that orbit and will not cross over into other ones.

The dotted orbit grid also provides a snapshot of the comets’ movement inward toward the black hole. Comets in a given orbital ring “X” can possibly appear in closer orbits, but in an altered form. As comets move closer to the central black hole, the increased gravitational force will break comets into pieces forming new smaller comets that are in the orbits closer to the center.

Comets break according to the following set of rules:

1) Comets whose length is 4 or more cells will break into two or more pieces with each piece having a minimum length of 2 cells. The combined length of all the pieces after the break must be equal to the size of the starting comet.

2) Comets whose length is 3 cells will lose one cell to produce a 2 cell comet.

3) Comets whose length is only 2 cells totally disintegrate and will not exist in the closer orbits. The 2 digits that made up this comet may appear adjacent to one another within a closer orbit, but they would need to be ordered in such a manner to avoid recreating the comet.

4) If the comet breaks into pieces that are not symmetric in size, the larger pieces must contain the larger digits. This rule also applies to the breaking of 3-cell comets which lose their smallest digit so that the 2-cells remaining contain the two larger digits of the starting three.

5) The sequence of digits that was in the original comet is always maintained in any surviving comet pieces.

The outermost orbit contains a comet of size 6: {1-3-4-5-6-7}.

In the middle orbital, this comet appears to have broken into two pieces: the 2-cell {1-3} and the 4-cell {4-5-6-7}. Within the rules, the only other valid possibility would have been for this comet to have broken into two 3-cell comets: {1-3-4} and {5-6-7}. A loss of one cell to produce the 5-cell comet {3-4-5-6-7} is not allowed by Rule 1 since it would imply that the comet broke into a piece with a length less than 2. A break into the 4-cell {1-3-4-5} and 2-cell {6-7} is not allowed by Rule 4 since the larger digits have to become part of the larger pieces following a break.

In the innermost orbit, there are only two pieces of the comet left: the 2-cell comets {4-5} and {6-7} which resulted from the breaking of the 4-cell comet in the previous orbit. The {1-3} comet no longer exists. This is the only possibility that can result from the 4-cell, 2-cell break found in the middle orbit.

In the actual puzzle grid below, all the given comets will follow these rules. For example, in the outermost orbit the 2-cell comets will cease to exist and each of the 3-cell comets will become one of the 2-cell comets in the next orbit which will then disappear.

In the innermost orbit there is only one 2-cell comet. This is the last remaining piece of a larger comet that exists in the outmost orbit. The form of this comet across all the other orbits needs to be deduced through solving the puzzle. None of the other comets already provided in the grid are part of this comet's transition from large to small.

To clarify that the 2-cell comet is the only comet located in the innermost orbit, there is a counterclockwise thermometer placed in all the other cells of the orbit. This thermometer is not a valid comet, but the regular thermometer rules still apply.

Thanks very much for trying the puzzle and I very much appreciate any feedback.

Click here to solve the puzzle using penpa-edit.