# Carcass Walking: An introduction

Carcass Walking is a grid puzzle inspired by the board game Carcassonne. The objective is to place the given cities into the grid, connect them with roads, draw one river across the grid, and find places for the given number of cloisters.

• The river (blue squares) runs from one edge of the grid to another in one continuous path which does not cross itself or branch out in multiple directions. It is possible to traverse the entire length of the river with vertical and horizontal moves without visiting any square more than once. Bridge squares (see below) count as part of the river.
• Cities (gray squares) are given shapes which must be inserted into the grid, rotated or reflected where needed. Cities cannot share an edge with the river, a bridge or another city, but may touch at a corner.
• Roads (red lines) connect all cities, forming a continuous network. Every city must be connected to every other city either directly by road, or by going through other cities via roads. Both ends of each road touch a city wall. A road cannot start and end at the same city, and it cannot cross itself or other roads or branch off into multiple directions.
• Bridges (red squares) are places where a road crosses over a river. Both the river and the road must continue straight through the bridge square without turning. Bridge squares are not counted as part of the road when counting road lengths.
• Cloisters (black squares) are placed in peaceful locations in the grid. A square is peaceful if it does not touch the edge of the grid and all of its eight neighbouring squares are empty (i.e. not part of a city, river, road, bridge or another cloister).
• The total number of bridges and cloisters, as well as the total length of all roads, must match the numbers given.
• Some squares are filled in from the start. Squares marked with "X" must be empty.

The puzzle:

• Does "x13 total" below the roads mean 13 of each row type, or 13 roads total? Oct 27, 2020 at 20:50
• 13 roads total. Hmm, how could I make it clear?
– Jafe
Oct 27, 2020 at 20:50
• @user39583 Augh, you're absolutely right. I need to fix this... Thanks for letting me know.
– Jafe
Oct 27, 2020 at 21:43
• Added an x on the bottom row.
– Jafe
Oct 27, 2020 at 21:49
• Is it permitted for a city to share an edge with a bridge, and must cloisters be surrounded by exactly eight empty squares or is an edge/corner-cloister permissible? Oct 28, 2020 at 2:13

NOTE: The cloister is a bit ill-defined. I am assuming cloisters cannot be adjacent, and cannot be along the edge either (reference to 8 surrounding squares).

The completed grid (road in pink):

Reasoning:

The first thing to notice is that since river and city squares cannot share edges, in the bottom left corner the river must pass through the three corner squares. Now, notice that there is a single bridge over which the road must pass. This forces the cities to be on opposite sides of the river. This forces the river to pass between the two given city squares, and also the left city to extend north from the given square. These force the diagram to look like so:

Now notice:

The river must past north of the city at right, and in particular must pass through column 6 no further south than the third row. The same statement can be made for column 5...the river could flow through the square diagonally northwest of the given city square at right, but then would have to go north. These conditions leave room for only one cloister in the first three rows, in either R2C2 or R2C3. This means the other cloister has to go south of the right city, in particular in space R7C6. Combined with the need for the river to come back down to the east of the right city, this forces the right city to also extend north from the given square. This forces much of the river, and also the second cloister:

Finishing up:

There must be 13 road pieces, going from one city to the other. On the left side, the road must emanate from the bottom or right side, since otherwise it would violate the cloister. This leaves four possible road squares. On the right, there are only 9 possible squares that could be roads without violating the cloister. So all of the possible road squares need to road squares, which forces the rest of the river and the bridge location, and finishes the puzzle.

• This is the intended answer. Nice work! I've edited the rules to clarify the cloister placement.
– Jafe
Oct 28, 2020 at 5:38