Logic Masters Deutschland e.V.

Rules:

1. Write digits from 0 to 9 in each region. Regions are defined as two orthogonally connected pentominoes. There are 10 regions that must be discovered by the solver. No two pentominoes of the same shape can touch each other, not even diagonally. Reflections and rotations are considered the same shape. Of course, all of the 12 different pentomino shapes must be in the grid (T, U, V, W, X, Y, Z, F, I, L, P, and N). The circles represent the highest left cell of each pentomino. All circles are given.

2. Draw a loop that can move orthogonally and diagonally in the grid. The loop must visit each circle, each pentomino exactly once and exactly 3 cells in each pentomino. The sum of these 3 cells are the same for each pentomino and must be deduced by the solver. The loop cannot cross itself and digits on the loop inside pentominoes are in ascending/descending order when there are several possible paths. Faulty digits represented by squares cannot be on the loop.

3. Big arrows starting from circles show the location of doublers. Circles without arrows are doublers themselves. Doublers double the cell's value for the purpose of the 3-cells sum. However, the cell value pointed by two arrows in r1c7 is tripled.

4. Circles that are connected along the loop are consecutive digits. (i.e. if a circle is 7, the previous/next circles in the loop are 6 or 8.) The only thing you know for sure is there is at least one 8 and at least two 0 in circles (at least one of the 0 is inside a circle containing a grey arrow).

5. Quantum radiations from outer space changed some numbers in the grid. This allows the grid to have some repeats in lines or columns. Small black arrows in a cell indicate that the digit in that cell is repeated once somewhere in each indicated direction. The repeated digit in that direction does not necessarily have an arrow pointing back to the other repeated digit. All repeats can be explained by these small black arrows. For an obscure reason, the loop cannot get out of a cell in the direction pointed by small black arrows.

6. Amazingly, it seems the bond of two pentominoes together transcend the universe and the bounds are so strong that radiation does not affect them. This means the grid has no repeat in regions.

Solve online (Penpa+) : Answer check is also enabled if you use blue or green colour digits

Solve online (SudokuPad)

Puzzle:

Happy Solving !!!