Enigma 343: In the mews
From New Scientist #1492, 23rd January 1986 [link]
Silent Mews, the cul-de-sac where I live, is dull and uniform. Every house on this side of the road has one exactly corresponding to it on the other side, and vice versa. The only exciting thing about it is that the houses are numbered boustrophedon. That is, starting at number 1 and visiting each house in numerical order takes you up one side of the street, along the end of the mews and back along the other side.
To lend my house individuality, I have bought brass numbers for my front door (all the other houses have plastic). Each digit costs the same, so it would cost 222 times what I paid for my door number to replace everyone else’s door numbers with brass. Not only does my property have a special number, but my number has a special property. Rearranging its digits produces exactly four numbers. One of these is my number and one is the number of another house in the mews.
If more houses were to be added on after the last house on the mews, it it would be possible for the set of digits in my number to be the only set which appeared in a total of exactly four house numbers, two of which were in the old part of the mews, and two which appeared in the newly extended part.
You may wonder whether, besides the houses on the two long sides of the mews, there are also houses at the blind end of the mews, but the answer to this should be obvious, as is the answer to this puzzle, namely: what is the number of the house directly opposite mine?
I am going to be away next week, but I will try and keep to the posting schedule if possible.