Enigma 1645: Neighbourhood watch
7 December 2011
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From New Scientist #2811, 7th May 2011 [link]
In my street the odd-numbered houses are on the left and the even-numbered houses are on the right. The first house on the left, number 1, is immediately opposite number 2, then number 3 is opposite number 4, and so on. Each house has its number on the gate.
On a recent walk I started at house number 1 and walked up the left-hand side of the road to the very end, then I crossed to the house opposite and walked back down the right-hand side until I reached my own house.
I counted the number of occurrences of the digit 1 that I had seen on the gates, and the number of occurrences of the digit 2: after entering my own gate the product of these two totals was a two-figure number.
Had I stopped counting at the house opposite my own, then the product would have been smaller; in fact it would have been the reverse of the eventual product.
What is my house number?