Enigma 1091: One’s best years
23 October 2017
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From New Scientist #2247, 15th July 2000 [link]
Mr Meaner has now retired from teaching. As a tough arithmetic exercise each year he used to ask his class to take the number of the year and find some multiple of it which consists simply of a string of ones followed by a string of zeros. For example in 1995 one girl in the class found that the 19-digit number 1111111111111111110 was a multiple of 1995!
Mr Meaner had been asking this question every year since he started training as a teacher. On the first occasion it was a reasonably straightforward exercise and most of the class found a multiple using as few digits as possible.
It is lucky that he did not ask the question a year earlier, for that year would have required over two hundred times as many digits as that first occasion did.
In what year did Mr Meaner first ask the question?