### Random Post

### Recent Posts

- Puzzle 67: Addition: letters for digits
- Enigma 1101: Disappearing numbers
- Enigma 410: Most right
- Tantalizer 475: League table
- Enigma 1102: The Apathy Party
- Enigma 409: Hands and feet
- Puzzle 68: Football and addition: letters for digits
- Enigma 1103: Brush strokes
- Enigma 408: Royal numbers
- Tantalizer 476: Take your partners

### Recent Comments

Jim Randell on Puzzle 67: Addition: letters f… | |

geoffrounce on Enigma 1313: Triangles | |

Jim Randell on Enigma 1313: Triangles | |

geoffrounce on Enigma 1313: Triangles | |

Jim Randell on Enigma 1313: Triangles |

### Archives

### Categories

- article (11)
- enigma (1,097)
- misc (2)
- project euler (2)
- puzzle (25)
- site news (42)
- tantalizer (25)
- teaser (3)

### Site Stats

- 161,924 hits

The following Python program runs in 130ms.

Solution:The sum of the products is 59136.The LCM of 28, 30, and 31 is 13020. If MONTH is to have five different digits it must be 78120, so MON = 781. We multiply that by a number between 26 and 38 to get a 5-digit product starting with T = 2. SAT and SUN are at least 342; SAT ends in 2 and must be multiplied by at least 77 (probably more) to obtain a 5-digit number starting with the same digit (and having 1 as its third). Furthermore, the second digit of each product is the same. That narrows the search somewhat.