70. |
I have a 2-digit number. If the order of the digits is changed, it makes a new number which is 1 less than one-half of my number.What is my number? |

71. |
A combination lock on a safe needs a 6-letter sequence to open the safe. This is made from the lettersA, B, C, D, E, Fwith none of them being used twice.
Here are three guesses at the combinationC B A D F EA E D C B FE D F A C BIn the SECOND guess only TWO letters are in their correct places. In the THIRD guess only THREE letters are in their correct places. Each of the 6 letters is in its correct place once. What is the correct combination? |

72. |
A chess-board is made up of 64 black and white squares in the normal way, each having an edge length of 5 centimetres. On this board the largest possible circle is drawn whose circumference lies completely in the white squares. What is the radius of the circle? |

The winner of Competition #23 was C. Dickinson of Middlesbrough.

The answers were:

67. | -40°F = -40°C |

68. | 23 different paths. |

69. | Sqrt(46.25) or 6.8 metres (to 1 dec.place) |