Challenge Level

Solutions gathered by Alan after RI lecture:

Polo total |
Number of distinct responses |

9 |
2 |

10 |
6 |

11 |
10 |

12 |
13 |

13 |
10 |

14 |
5 |

15 |
12 |

16 |
8 |

17 |
3 |

18 |
3 |

In fact, Cecilia, Anna and David have emailed us to say that they think the above table isn't quite right.

They suggest the following:

Polo total |
Number of distinct responses |

9 |
3 |

10 |
6 |

11 |
10 |

12 |
13 |

13 |
10 |

14 |
10 |

15 |
13 |

16 |
10 |

17 |
6 |

18 |
3 |

They say:

It is possible that we lack some solutions, but what is absolutely certain is that the list must be symmetric since for every solution in which each row and column add N we can find a solution in which each row and column add 27-N, with the following procedure:

a b c 9-a 9-b 9-c

d e 9-d 9-e

f g h 9-f 9-g 9-h

Thank you!