In Pentomino equations - a puzzle cache I discussed the 12 pentominoes, which are geometric figures composed of 5 squares of the same size joined along their edges. More generally, a polyomino is a figure composed of any number of squares of the same size joined along their edges.
For this puzzle, we'll only be dealing with a special type of polyominoes, called "snakes". In a snake, there are two "end" squares, each of which shares an edge with exactly one other square; the other squares in the snake form a single path from one end to the other. Each of the intermediate squares shares an edge with exactly two other squares in the snake, so as you move from one end to the other there's never any choice about which way to go. Furhermore, a snake can't have any holes; you can move from any point that's not part of the snake to any other such point without crossing the snake.
Here are some examples, showing all possible snakes made up of 2 to 6 squares, and five larger ones:
To further clarify the definition, here are three polyominoes that are not snakes:
Figure 1 is not a snake because it has no end cells; each of its 4 squares shares an edge with 2 others. Figure 2 fails because 2 of its squares (shown in grey) share edges with 3 other squares. Figure 3 fails because it has a hole.
Figure 4 below shows a 5 by 5 square that's been cut into 3 snakes, of sizes 6, 9, and 10. I've marked one end of each snake with its size. To make a puzzle out of this, I'd just show you the 3 numbers, as in Figure 5, and ask you to figure out the shapes of the snakes. But it wouldn't be a very good puzzle, since it has 2 other solutions, shown in Figure 6.
Unlike the sample puzzle above, the puzzle below has a unique solution. Here I've cut an 8 by 8 square into 5 snakes, of sizes 3, 5, 8, 23, and 25. As in the example above, each number is in one of the end squares of its snake, not somewhere in the middle.
Once you've figured out the shapes of the snakes, let:
A be the number of squares in column 6 that are in the snake of size 25;
B be the number of squares in row D that are in the snake of size 25;
C be the number of squares in row E that are in the snake of size 23;
D be the column number of the other end of the snake of size 23;
E be the number of squares in row H that are in the snake of size 23;
F be the number of squares in row E that are in the snake of size 25.
The cache is at
N 40° 50.ABC W 124° 10.DEF
If you think you've figured out the coordinates, you can check them with certitude:
You can also see who else has solved the puzzle. Note: You can remain anonymous if you want to; incorrect guesses are always anonymous. (Puzzle makers, you can create your own certitude links here.)
If Certitude isn't working, you can use GeoCheck instead:
Congratulations to the first certified solver, turuthok, and the first finder, humspuds.