Enigma 1140: A long, long road
21 November 2016
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From New Scientist #2296, 23rd June 2001 [link]
George lives in a long road in which the houses are numbered from one with no numbers missing. He has calculated that the total of all the house numbers less than his is equal to the total of all the house numbers greater than his.
George’s brothers, Dave, Ernest and Fred, live in shorter roads than George, but they can each make the same claim regarding house numbers. The brothers’ four house numbers have different numbers of digits.
Hearing this story, George’s drinking friend scribbled on a beer mat for a while, then he asked: “George, does your road have nearly 10,000 houses?”
“No, not nearly that many,” George replied.
How many houses are there in total in the four roads? And what answer would the man in the pub have given to that question before being corrected?