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A year is called interesting if it consists of four distinct digits. For example, the year 2019 is interesting. All years from 2013 up to and including 2019 are interesting: a sequence of seven consecutive interesting years. Determine the next sequence of seven consecutive interesting years and prove that this is indeed the next such sequence.

 Jan 18, 2021
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2103, 2104, 2105, 2106, 2107, 2108, 2109

 

Since we can't have any numbers in the 2020-2029, section, 2030 is next. We can't have anything below or equal to 2033 because it would eventually run into 2033. But with 2034, there is just not enough space to finish. Same for the next. The 2090s would be 2093, 2094, 2095, 2096, 2097, 2098, and 2099.

So we go into the next century. We cant have 1 or 2 so 2103 and on will work.

 Jan 19, 2021

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