Pathfinder (Crossword Type)

Pathfinder is a variety crossword puzzle format in which entries follow winding paths through the puzzle grid, which solvers must deduce as they go along. Pathfinder puzzles are usually presented on a square grid, although hexagonal variants are also used.

Background

Pathfinder puzzles appeared in Games Magazine at least as far back as the early 1990s, which featured puzzles written by Mike Shenk. It is unclear when exactly Pathfinder puzzles originated, and whether Shenk was the originator of the format.

Puzzle Application

Presentation

A Pathfinder puzzle typically has a square grid with some black squares. However, unlike a crossword puzzle, the black squares in a Pathfinder puzzle do not delimit the beginning and ends of words, but are there to break up the pattern of uninterrupted white squares. The black squares are usually placed so that all white squares are connected, and every white square is orthogonally adjacent to 2 or 3 other white squares. In practice, this typically means that every other square in every other row is shaded black in a staggered pattern, for a total of 25% black squares (or slightly less). In theory, a Pathfinder grid could be presented with fewer black squares, but the black squares serve to limit the possibilities for answer placement, and with fewer black squares the challenge would be undesirably high. In contrast, the addition of more black squares would make the paths too restricted. Because of the standard shading pattern and desired symmetry of the blank grid, most Pathfinder puzzles use an 11 by 11 square grid, with some extra-large puzzles using a 15 by 15 grid. Other grid sizes are possible, but again given the shading pattern and symmetry constraints it is easiest to have a grid with an odd number of columns, and a number of rows that is 3 more than a multiple of 4. Depending on the shading pattern, an 11 by 11 square grid will usually have between 89 and 94 white squares.

The grid for a Pathfinder puzzle is also labeled with numbered squares. Like a standard crossword puzzle, the numbers indicate the squares where each entry begins. Unlike a standard crossword, the answers are not restricted to reading across and down, and will instead start going in any direction, and then make one or more turns through the grid. Typically, the starting direction for each entry is given as part of the clue; a clue that begins "1E" indicates an entry beginning at square number 1 and proceeding to the east (i.e., to the right). Any subsequent changes of direction are not indicated, though it is typical for the clues to supply either answer lengths and tags or full enumerations. It is possible for two entries to begin in the same numbered square, and they may or may not share the starting direction. Additionally, some elements can be added to the presentation to make answer placement easier. The squares where entries end may be indicated with black dots, or numbers may be placed in both the beginning and ending squares of each answer, with the clues indicating both the beginning and ending squares.

Pathfinder puzzles can also be presented on a hexagonal grid. In a hexagonal grid, roughly one-third of the cells will be shaded black, and there are six possibilities for the starting direction, usually listed as NE, E, SE, SW, W, and NW. On a hexagonal grid, every white space will be adjacent to exactly three other white spaces, unless it is on the edge of the grid. In contrast, many white squares in the interior of a square Pathfinder are only adjacent to two other squares, which means that hexagonal grids have a bit more freedom in the placement of entries. Typically a hexagonal Pathfinder will use a grid with 8 hexes on each side, but larger grids with 10 hexes on a side are also common.

Regardless of the grid shape, in a completed Pathfinder each white space will be filled with a letter that is used in exactly two entries.

Difficulty

Pathfinder puzzles are among the more difficult variety formats. The added degrees of freedom for entering answers into the grid makes correctly placing entries a significant challenge. The number of possible paths for entering longer entries grows exponentially, and even when additional information like the ending square is given there may be dozens of potential ways to enter an answer in the grid.

In addition to the sheer number of possible paths for entering an answer, the freedom also adds a lot of uncertainty to verifying checked answers in the grid. Unlike many types where it can be determined where two given entries will cross with a reasonable amount of confidence, it is difficult to determine where two entries in a Pathfinder grid will cross, if at all. Two sufficiently long entries beginning at opposite corners of the grid may overlap in the middle, while two entries beginning in adjacent squares might not intersect at all. Additionally, grid entries that do intersect may have any number of letters in common, which might be read in the same direction or in opposite directions.

Nevertheless, many solvers enjoy the challenge of teasing out a Pathfinder grid, and it can be very rewarding to figure out how everything fits together.

Strategy

Because there are so many degrees of uncertainty in the placement of answers in a Pathfinder, solvers need to be careful at all times. When solving a Pathfinder, a solver should first look out for clues with answers that they are sure of. Because the starting square and direction of each entry is given with the clue, placement of the first two letters of the answer can be determined with complete certainty. Additionally, the shape of the grid might constrain one or more additional letters at the beginning; an entry near the corner of a square Pathfinder grid can have the placement of as many as the first 6 letters forced. However, you should not make guesses as to the placement of any letters that are not forced at this stage.

Then, it is useful to look at sections where two entries are potentially occupying the same space. Any arrangement that would yield a conflict can be eliminated. For example, if the first two letters of the entry NOISY have been placed, and the third letter could continue to the right or to the left, but the square to the left is the beginning of the answer HERRING, then NOISY must continue to the right to avoid conflicting with the H already placed in the grid. It might also be the case that choosing a particular direction for the third letter of NOISY forces the placement of the fourth letter, which could also come into conflict with another entry. However, even if a particular answer placement would have two answers properly sharing the same letter, that does not mean it is necessarily the correct placement. Answers that could potentially overlap in a single shared letter, or even in longer substrings (especially common substrings like ER of ING), might not actually overlap in the solution. It may be worth making some guesses where two entries might overlap in a longer or more unusual substring, but at this stage, the solver should still focus on eliminating the impossible.

Solvers should also keep track of how often a given letter in the grid has been used. Each letter in a standard Pathfinder is used in exactly two answers, so if two entries are confirmed to overlap in one or more squares than any other nearby entries cannot used those shared letters. Additionally, if the placement of overlapping entries would leave an unchecked letter surrounded by checked letters, it would be impossible to check that letter, so the placement must be incorrect. It is recommended that solvers keep track of checked letters by making a mark in a square when it has been used by two different entries, though accurate bookkeeping can be difficult if the solver needs to backtrack, or has answers that are only partially placed. Additionally, a Pathfinder appearing in a puzzle hunt may have unchecked or overchecked letters, or entire answers that are unclued, making bookkeeping even more of a challenge.