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Programming Enigma Puzzles

1 April 2019

Posted by on **From New Scientist #1644, 24th December 1988** [link]

The five couples in Yuletide Close send cards to some of their neighbours. Some of them told me who (apart from themselves) send cards.

Alan:“The cards not involving us are the ones exchanged between Brian’s and Charles’s houses, the ones exchanged between Brian’s and Derek’s, the card from Charles to Derek (or the other way round, I’m not sure which) and the card from Brian to Eric (or the other way round).”

Brenda:“Apart from our cards, Alice and Emma exchange cards, as do Dawn and Christine, and Dawn sends Emma one.”

The Smiths:“The cards not involving us are the ones exchanged by the Thomases and the Unwins, those exchanged by the Williamses and the Vincents, the one from the Thomases to the Williamses and one between the Unwins and the Vincents (but I forget which way).”

No 3:“Nos 1 and 5 exchange cards, one card passes between Nos 2 and 4 (I don’t know which way) and No 2 sends one to No 1.”Charles Thomas receives the same number of cards as he sends. On Christmas Eve, he goes on a round tour for drinks. He delivers one of his cards, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, takes one of their cards and delivers it, has a drink there, collects the card from them to him and returns home, having visited every house in the close.

Name the couples at 1-5 (for example: 1, Alan and Brenda Smith; 2, …).

**Enigma 1321** is also called “Christmas cards”.

This completes the archive of *Enigma* puzzles from 1988. There is now a complete archive from the start of *Enigma* in 1979 to the end of 1988, and also from February 1999 to the final *Enigma* puzzle at the end of 2013. There are 1265 *Enigma* puzzles posted to the site, which is around 70.8% of all *Enigma* puzzles published.

[enigma493b] [enigma493]

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This Python program runs in 100ms.

Run:[ @repl.it ]Solution:The residents of the close are:The card exchanges are (3 bidirectional, 3 unidirectional):

Charles’s walk is: 2 → 1 → 5 → 3 → 4 → 2.