or,

** And the subheading should suggest what's coming...**

**Can we find a base in which 21 can be divided by 12 without remainder? And why should we? - Because someone said it couldn't be done. They may well have meant that it can't be done if the base is a positive number - and in fact, if you use base (-5) then 21 = 3 x 12 is true.**

**
Which led me to look at some other results in other bases - not recent discoveries, I might add; the keyboard is ready and willing to work, but occasional bursts of lethargy often hit the typist, in particular Nap Attacks as favoured by Garfield. ^{1}**

**
31 = 2 x 13 (base 5)
41 = 3 x 14 (base eleven)
51 = 3 x 15 (base seven)
51 = 4 x 15 (base nineteen)**

**
In tabular form:**

Number | Bases |

31 | 5 |

41 | 11 |

51 | 7, 19 |

61 | 29 |

71 | 9, 17, 41 |

81 | 13, 55 |

91 | 11, 31, 71 |

T1 | 23, 89 |

E1 | 13, 19, 29, 49 |

and here are some with 2 as unit-figure | |
---|---|

52 | 8 |

72 | 19 |

82 | 11 |

92 | 34 |

T2 | 19 |

E2 | 14, 53 |

(to be continued)