### Random Post

### Recent Posts

- Tantalizer 450: Marriage problems
- Enigma 1057: Recycled change
- Enigma 452: Figure out these letters
- Puzzle 46: I lose my specs
- Enigma 1058: A row of colours
- Enigma 451: Double halved
- Tantalizer 451: Death rates
- Enigma 1059: Century break
- Enigma 450: A pentagonal problem
- Puzzle 48: Verse on the island

### Recent Comments

Jim Randell on Tantalizer 450: Marriage … | |

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… |

### Archives

### Categories

- article (11)
- enigma (1,183)
- misc (2)
- project euler (2)
- puzzle (46)
- site news (46)
- tantalizer (50)
- teaser (3)

### Site Stats

- 184,974 hits

Advertisements

This is a slightly different approach from my original Perl program that I wrote when the puzzle came out [link]. It’s shorter and faster and runs (under PyPy) in 9.2s. If I’d started off using this approach I probably wouldn’t have bothered writing the C version.

Solution:(a) 9 tiles; (b) 11 tiles.The solution for 9 tiles is a 15×25 grid (for example):

And for 11 tiles it is a 22×29 grid (for example):

If you stop the program from returning as soon as it has found a solution the program finds 336 possible tilings for the 15×25 grid and 64 possible tilings for the 22×29 grid (although this takes no account of symmetrical solutions, so you can divide these numbers by 4 to get the number of essentially different solutions – 84 for the 15×25 grid and 16 for the 22×29 grid).

The next smallest two possible tilings are both with 14 tiles and are for a 25×49 grid and a 35×35 grid.