Around the houses
Fewer than 100 houses have been built on the edge of a circular green, equally-spaced around the whole perimeter and numbered 1, 2, ... in order. I have counted the number of pairs of houses with their first and second digits exchanged that are either 90 degrees or 180 degrees apart around the circle. The numerical difference between the counts for 90 degrees and for 180 degrees apart is the same as the higher digit of the lowest-numbered house involved.
How many houses are there in all?
WIN £15 will be awarded to the sender of the first correct answer opened on Wednesday 8 January. The Editor's decision is final. Please send entries to Enigma 1778, New Scientist, Lacon House, 84 Theobald's Road, London WC1X 8NS, or to
Answer to 1772 Clueless: The two answers are 44454 and 45444
The winner Elliott Line of Coventry, West Midlands, UK
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