Introduction

Numerous newspapers make available equivalents of our Tracks puzzle game which we describe here. At the start of a game players are presented with a grid containing a few clues in the form of track sections, two of which connect to the grid edge. The object of the game is to find the unique path which passes between these two edge clues and, without intersecting itself, passes through all the other clues. As a vital aid, the row of numbers along the top of the grid and the column down the right hand side contain the counts of the number of track sections which should appear in each column and row when the puzzle is completed correctly.

Contents

Tracks Example 1

Tracks Example 1

A screenshot from a partially completed tracks puzzle. It shows an 8x8 grid with the clues coloured red and the cells filled by the player in blue. The player has made good use of the track counts for rows and columns to place 'x' symbols in cells where the track cannot go and 'o' symbols where the track must pass.

When the player moves the cursor over a cell in the grid, shapes will appear showing the cell's possible track shapes. The shape shown will depend on where within the cell the cursor is positioned. Left clicking on the mouse will set the current shape as the guess for the cell.

The game contains 500 puzzles: 100 6x6, 200 8x8, 100 10x10 and 100 12x12. However, the game also offers an unlimited number of puzzles, as it can create them very quickly. This is initiated if the player enters a negative puzzle number. To be used in conjunction with this there is an option in the menu for selecting the grid size for the randomly generated puzzles.

Tracks Example 2

Tracks Example 2

A screenshot from a completed tracks puzzle. It shows an 8x8 grid with the clues coloured red and the cells filled by the player in blue.

Playing

The jigsaw symbol is a menu which contains options to choose the grid size, the font size, to set the colours of all the games components and for saving the configuration. A left click on the PZL tracks symbol next to the jigsaw starts a new game by loading a randomly selected puzzle. Alternatively a right click on this symbol will load the next puzzle. A click on the wand requests a hint. The game finds a cell for which the solution can be deduced from the current state of the grid and shows it with a '?'. If the player can work out which is the correct shape/symbol for the cell they can add it using a left click. Otherwise a further click on the hint button will cause the shape/symbol to be added. While the hint is active (shown by the wand icon leaning leftwards) clicking on the wand with the middle mouse button will cause a pop-up to appear containing a short explanation of the hint. If a hint is requested when the grid contains errors, no hint will be given, the thumb icon turns down and the incorrect cells are identified. They can be removed using right clicks or by a single click on the thumb icon. At any time clicking the thumb checks the current grid for errors, a second click will remove them. The sad smiley will display the solution. The entry box contains the current puzzle number and can be used to enter numbers. To its right is a clock. If a hint is displayed a number code (0 - 6) indicating the hint algorithm used will replace the text of the clock until the hint is applied.

The program starts with a randomly selected puzzle displayed. When the player moves the cursor over a cell in the grid, shapes will appear showing the cell's possible track shapes. The shape shown will depend on where within the cell the cursor is positioned. By moving the cursor in the cell the player will quickly learn where in the cell to position the cursor in order to produce the wanted shape. In addition to the 6 track shapes the letters 'o' and 'x' also appear. 'o' means this cell is part of the path and 'x' means that this cell is not part of the path. A left mouse click will add the shape or letter to the cell. Right click will remove any previously placed symbol or shape.

Tracks Worked Example

A video from tracks being played by an elderly person with shaky fingers. First they select the puzzle number they want to work on. Then they start by filling with 'x' symbols the cells which cannot be part of the path and then, using 'o', those that continue clues. This is followed by marking the continuations of the clue cells which in turn completes the quota of track cells for more rows and columns. At one point they request a hint but shaky fingers produce a double click by mistake and the solution for the cell is given. Eventually segments of the path are obvious and as they are filled in the rest becomes clear. Notice that the shape or symbol produced depends on the position of the cursor within the cell.

Algorithms

The algorithms used by Tracks are explained using examples. We were surprised that such simple algorithms could produce and solve such convoluted pathways. When the player requests a hint the program displays a "?" in a cell whose answer can be deduced from the current state of the puzzle. Below we show one hint example for each algorithm, and to its right the solution for the highlighted cell. The algorithms are named 0 to 6.

Alg_0

Alg_0

If a row or column has all its tracks, we can fill the remaining cells with 'x'.

Alg_1

Alg_1

If a cell is receiving track from an adjacent cell, mark it with 'o' so we know it is part of the track, even though we don't know of what type.

Alg_2

Alg_2

Special cases. Here there can be no path through the cell with the '?'.

Alg_3

Alg_3

If a cell is empty check if its track must exit in only one direction.

Alg_4

Alg_4

If a cell is known to be in the path (ie is set to 'o') check to see if is can only continue in a particular direction.

Alg_5

Alg_5

If the number of unset cells in a strip equals the number of path cells still required, they must all be 'o'.

Alg_6

Alg_6

To be part of the track a cell must have two neighbours which must also be part of the track. If that is not possible the cell is not part of the track.