# Sunday Times Teaser 2905 – Trackword

*by Danny Roth*

#### Published May 27 2018 (link)

George and Martha are tackling a Trackword problem which appears in magazines. Nine letters are placed in a 3×3 grid and you have to work from one square to a neighbour, proceeding up, down, left, right or diagonally until all nine squares have been visited to form a nine-letter word. You must start in the top-left corner. As an example, you can get the word **EIGHTFOLD** from the following grid:

E |
T |
H |

F |
I |
G |

O |
L |
D |

George and Martha thought that would be interesting to work out how many possible routes there are which start in the top-left corner.

How many routes are there?

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Erling Torkildsen provides a GeoGebra model for this teaser here.

There’s a handy grid_adjacency() function in the

enigma.pylibrary [ http://www.magwag.plus.com/jim/enigma.html ] to compute the adjacency matrix on a square grid.The code can be executed on repl.it [ https://repl.it/@jim_r/teaser2905 ].

From square 0 we can go to to the central square (4) or to an edge square (1 or 3), so we can just count the paths with prefix [0, 4] and [0, 1]. There will be the same number of paths with prefix [0, 3] as there are with prefix [0, 1].