# Pilgrims' Plot

This cross-number puzzle is one of my all-time favourites. I first came across
it in a book called "Games for the Superintelligent", by James F Fixx. It
looks impossible to solve, but the numbers and clues are cleverly interlocked
so that by using a bit of logic, calculation and trial-and-error it can be
cracked.

## The puzzle

The year is 1939. On Farmer Dan's farm is a rectangular plot of land called
Pilgrims' Plot that is ripe for development as a new football ground. For
those of you not familiar with old units of measurement 1 acre = 4840 square
yards, 4 roods = 1 acre, 1760 yards = 1 mile. There are also 20 shillings in
£1.

### Across

1. | Area in square yards of Pilgrims' Plot |

5. | Age of Martha, Farmer Dan's aunt |

6. | Difference in yards between the length and breadth of Pilgrims' Plot |

7. | Number of roods in Pilgrims' Plot times 8 down |

8. | The year Farmer Dan's family acquired Pilgrims' Plot |

10. | Farmer Dan's age |

11. | Year of Mary's birth |

14. | Perimeter in yards of Pilgrims' Plot |

15. | Cube of Farmer Dan's walking speed in mph |

16. | 15 across minus 9 down |

### Down

1. | Value in shillings per rood of Pilgrims' Plot |

2. | Square of the age of Farmer Dan's mother in law |

3. | Age of Mary, Farmer Dan's daughter |

4. | Value in pounds of Pilgrims' Plot |

6. | Age of Dan junior, Farmer Dan's son, who is twice the age of his sister Mary in 1945 |

7. | Square of the breadth of Pilgrims' Plot |

8. | Time in minutes it takes Farmer Dan to walk 1 1/3 times around Pilgrims' Plot |

9. | The number that multiplied by 10 across gives 10 down |

10. | See 9 down |

12. | Addition of the digits of 10 down plus 1 |

13. | Number of years Pilgrims' Plot has been in Farmer Dan's family |

## The solution

Here are some details to get you started on the solution. The two years (8
across and 11 across) must start with a 1. 15 across is a cube and the only
two digit cubes are 27 and 64. 16 across must therefore end in either a 6 or a
3, but as 7 down is a square number then it must be a 6 as no square numbers
end in 3. Therefore 15 across is 27 and sixteen across is 16 and 9 down is 11.
9 down (11) times 10 across equals 10 down, which ends in a 2, so the second
digit for 10 across is also a 2. So 8 down is 12 and the perimeter of
Pilgrims' Plot can therefore be walked in 9 minutes, which at 3 mph means the
perimeter (14 across) is 792 yards.