### Random Post

### Recent Posts

### Recent Comments

Brian Gladman on Enigma 1057: Recycled cha… | |

Jim Randell on Enigma 1057: Recycled cha… | |

geoffrounce on Enigma 452: Figure out these… | |

Jim Randell on Enigma 452: Figure out these… | |

Jim Randell on Enigma 1627: A riddle for the… |

### Archives

### Categories

- article (11)
- enigma (1,183)
- misc (2)
- project euler (2)
- puzzle (46)
- site news (46)
- tantalizer (49)
- teaser (3)

### Site Stats

- 184,903 hits

Advertisements

If we suppose the dimensions of the park are

xandy=x+ 25 and the paths have lengtha, as shown in the diagram.Then we can see from the similar triangles that:

hence:

(You can also see this by moving the triangles to make a square park with sides

a).And in order for the paths to meet inside the park we require:

The following simple Python program finds the first integer

xthat satisfies the conditions. It runs in 31ms.Solution:The paths are each 156 metres long.To solve a more general problem where the dimensions of the park are

xandx + nyou can use an approach suggested by Brian in this post [ http://www.newenigma.com/enigma/view_enigma.php?id=1758#response7871 (registration required) ] by considering the factors ofn².This Python program lets you specify

non the command line (default is 25, as in the original Enigma puzzle), and returns all possible solutions (there may be none, e.g. whenn=20, or there may be more than one, e.g. whenn=45).