### Random Post

### Recent Posts

### Recent Comments

Brian Gladman on Enigma 1057: Recycled cha… | |

Jim Randell on Enigma 1057: Recycled cha… | |

geoffrounce on Enigma 452: Figure out these… | |

Jim Randell on Enigma 452: Figure out these… | |

Jim Randell on Enigma 1627: A riddle for the… |

### Archives

### Categories

- article (11)
- enigma (1,183)
- misc (2)
- project euler (2)
- puzzle (46)
- site news (46)
- tantalizer (49)
- teaser (3)

### Site Stats

- 184,903 hits

Advertisements

This Python program runs in 65ms.

Solution:ENIGMA = 163072 (= 416 × 392).A permutation solution also works, but takes a few seconds longer:

The problem can be recast as a long division sum, and then the

SubstitutedDivision()solver fromenigma.pycan be used on it. This program runs in 99ms.hi can u please explain the logic how to solve

The basic idea is to substitute the letters for (different) digits, so that the long multiplication sum makes sense. This means the assignment of letters has to be chosen such that the intermediate products also make sense. (The puzzle presents them in the opposite order I would have expected, which is why I re-wrote the sum in the initial comment of my first program).

You can do this with pencil and paper or write a computer program to do it for you. My programs try possible assignments of letters to digits, until it finds one that gives a sum that fits the diagram.