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# Treebeard's Stumper Answer23 Jan 98

Double-Digit Years

1998 has two 9's, as do all the years in the 90's. But when are the last and next years that don't have any repeated digit? Between those dates there is a run of 25 consecutive double-digit years. When is the next time that there will be such a run of double-digit years? The longest possible run of unique-digit years is just 10, for example the years 1-10 or 12-21. Adding any century digits would only force an early match, so 10 is the limit. But what is the longest run of double-digit years since the year 1 A.D. and into the future?

1987 was the last year with no repeated digits, and 2013 will be the next, with a run of 25 double-digit years in between. This won't happen again until the 102 year span between 2199 and 2300. The longest run since the year 1 A.D. was the 104 years between 1099 and 1202. There will be some very long runs of double- digit years in the distant future, including every year after 9876543210 A.D. (Why?) I believe that 1098765433 to 1203456788 is the longest period before that.

I wrote a quickie Basic program to find long runs of double-digit years. It's interesting how the percentage of double-digits increases with the years. 38% of the years before 1998 have repeated digits, but this increases to 47% of the years to 9999, 68% of the years to 99999, and 99%+ of all the years to 9999999. What about different number bases?

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