There are four different cubes clocks. The first one displays the standard time with 4 cubes. The second one presents the military time with 5 cubes. The third and fourth clock use the standard time including am/pm with 5 or 6 cubes.

TBD: manual demo

TBD: automatic clock

TBD: manual demo

TBD: automatic clock

TBD: manual demo

TBD: automatic clock

There are 4 positions:

- The first position is blank or '1'.
- The second position can be each digit.
- The third position is a digit from '0' up to and including '5'.
- The fourth position can be each digit.

The tabel gives the number of occurrences of each digit.

time | digit | # |
---|---|---|

10:00 | 0 | 3 |

11:11 | 1 | 4 |

2:22 | 2 | 3 |

3:33 | 3 | 3 |

4:44 | 4 | 3 |

5:55 | 5 | 3 |

6:x6 | 6 | 2 |

7:x7 | 7 | 2 |

8:x8 | 8 | 2 |

9:x9 | 9 | 2 |

1:23 | blank | 1 |

total | - | 28 |

In total there are 28 digits needed to make all different possible.times. This is four more than the 24 cube sides. It is necessary to reduce the number of digits. Which way can this be done?

- The digits 6 and 9 are special. When 6 is turned 180 degrees you get 9. This means that the 6 can be used as 9. This reduces the number of necessary numbers with two.
- The digits 2 and 5 are also special, but it impossible to turn a cube to make a five from a two or a two from a five. The digits are a line mirroring. This cannot be used to reduce the total.
- The digit 0 is used only once three times. This is in "10:00".
Are there ways to display this time in such a way that maximaal two digit 0 are used and
that it is still clear that it is 10 o'clock?

Three possible solutions "10: 0", "10:-0" and "10:--".

Each solution reduces the number of used digits with 1 to 25. - The blank side of the cube is not necessary as it is also possible to just remove the cube from the display. This reduces the number of used digits with 1 to 24.

But is it possible to divide the digit over the cubes in such a way that all possible times can be displayed? Yes, there are several solutions.

The used solution is: Some examples:

Examples with real cubes:

There are 4 positions:

- The first position is '0', '1' or '2'.
- The second position can be each digit.
- The third position is a digit from '0' up to and including '5'.
- The fourth position can be each digit.

The tabel gives the number of occurrences of each digit.

time | digit | # |
---|---|---|

00:00 | 0 | 4 |

11:11 | 1 | 4 |

22:22 | 2 | 4 |

x3:33 | 3 | 3 |

x4:44 | 4 | 3 |

x5:55 | 5 | 3 |

x6:x6 | 6 | 2 |

x7:x7 | 7 | 2 |

x8:x8 | 8 | 2 |

x9:x9 | 9 | 2 |

total | - | 29 |

In total there are 29 digits needed to make all different possible.times. This is five more than the 24 cube sides. It is necessary to reduce the number of digits. Can this be done?

- The digits 6 and 9 are special. When 6 is turned 180 degrees you get 9. This means that the 6 can be used as 9. This reduces the number of necessary numbers with two.
- The digits 2 and 5 are also special, but it impossible to turn a cube to make a five from a two or a two from a five. The digits are a line mirroring. This cannot be used to reduce the total.
- The digit 0 is special as the value is zero. The normal way of presenting 10 o'clock is "10:00", but also "10:--" will be understood. This reduces the number of necessary numbers with another two.

The chosen solution is to present the time with 5 cubes, whereby the third cube is used to present the semi column. Some examples:

Examples with real cubes:

It is preferred to always use all cubes. The space needs be presented with a blank side in that case. The standard time ranges from 12:00 AM to 11:59 PM.

There are 6 positions:

- The first position is blank or '1'.
- The second position can be each digit.
- The third position is a digit from '0' up to and including '5'.
- The fourth position can be each digit.
- The fifth position is a 'A' or 'P'.
- The sixth position is a 'M'.

- As with the other solutions, the digits 6 and 9 are covered with the only one digit: 6.
- The characters 3 and M are also special. When you turn the 3 90 degrees, you will get the M. So you can cover the 3 and M with only one digit: 3.

Examples with real cubes:

standard 4 | standard 5 | military | standard 6 |
---|---|---|---|

1200 | 1200 MID/NIGHT | 00:00 | 1200MN |

1201 | 1201 AM | 00:01 | 1201AM |

1259 | 1259 AM | 00:59 | 1259AM |

100 | 100 AM | 01:00 | 100AM |

101 | 101 AM | 01:01 | 101AM |

959 | 959 AM | 09:59 | 959AM |

10 0 | 10 0 AM | 10:00 | 1000AM |

10-0 | 10-0 AM | 10:00 | 1000AM |

10-- | 10-- AM | 10:00 | 1000AM |

1001 | 1001 AM | 10:01 | 1001AM |

1159 | 1159 AM | 11:59 | 1159AM |

1200 | 1200 NOON | 12:00 | -N00N- |

1201 | 1201 PM | 12:01 | 1201PM |

100 | 100 PM | 13:00 | 100PM |

1159 | 1159 PM | 23:59 | 1159PM |