Logic Masters Deutschland e.V.

This puzzle was made in response to the CtC discord's monthly prompt, which was "pathfinding," particularly suggesting puzzles with non-looping snakes. Thanks to several people in the CtC discord for testing and feedback. The main version of this puzzle has background images that might be distracting or create legibility issues for some. One tip for legibility is to use the SudokuPad app to color these cells, but you can also play a symbolic version of the puzzle. If you'd like, you can also increase the difficulty. RULES:

Normal Sudoku Rules Apply

There is a hero (r8c8) who must clear the dungeon of five monsters and then reach the treasure chest (r8c2). Draw a path from the hero to the chest according to the following rules:
The hero may only move orthogonally, cannot visit the same square twice, and may travel between rooms (marked 3x3 boxes) only through the purple doors.
Doors separate digits of opposite parity (even/odd) even if not on the path.
All of the digits on the hero's path in a particular room add up to the hero's hit points (HP) at the time they enter (or start in) the room. The hero's starting HP must be determined by the solver and may not fall to zero or lower. The hero must defeat every monster in the dungeon before reaching the treasure.
Combat rules: The first cell in the hero's path that is adjacent (including diagonally) to a monster AND is in the same room as the monster (this may be the monster's cell) initiates turn-based combat. Monsters attack first and do damage (subtract from the hero's HP) equal to the digit in their circle, and the hero does damage (subtracting from the monster's HP but not their damage) according to the digit in the cell on the path that initiated combat. Monsters have starting HP equal to the digit in their circle and are defeated when their HP falls to zero or lower.
Example: Suppose the hero walks through the door from r2c3 to r2c4 with 35 hit points (so the digits in the path in box 2 total 35) and suppose that r2c4 = 4. This would initiate combat with the monster in r3c4 which has a 9 in its circle. The monster will deal damage 3 times (as it will take the hero 3 hits to kill the monster: 9 - 4 = 5; 5 - 4 = 1; 1 - 4 less than 0) dealing 9 x 3 = 27 points of damage. The hero will leave the room with 35 - 27 = 8 hit points remaining, and so the digits on the path in the next room they enter will sum to 8.


HINTS: (Highlight to view)

What's the minimum HP you need to have to reach the treasure chest?

No, it's not 3.

What's the minimum HP the hero will lose fighting monsters?

No, it's not 29.

What's the most HP the hero can start with?

No, it's not 45.

What's the most HP you can start with in box 8?

From box 2, there are in theory 2 potential paths (at the room by room level) to the treasure, but one of them will let you have enough HP to traverse each room.

Once you have the room-by-room path laid out, the digits on the path (but not necessarily where they are) should be known for most of the later rooms. But remember that to get here you have to kill all monsters but one in a single hit.

Don't forget that you know what row 1 is in in boxes 6 and 9.

After placing most of the digits at the end of the path, you'll have to look somewhere else. You know the path sums in boxes 2 and 3, and that's much more restrictive than it may first appear.