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It depends on the amount of leap years during that period. During a period of 7 years there is at least one leap year, and sometimes two. If there were two leap years, it would skip two days, so be 9 days after a Thursday, which is a Saturday. The 1st of January 1998 was a Thursday, and the 1st of January 2005 was a Saturday, because there were two leap years between 1998 and 2005, which were 2000 and 2004. It is not always the case though. The 1st of January 2009 was a Thursday, but the 1st of January 2016 is a Friday, because there is only one leap year between 2009 and 2016, which is 2012.

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Q: Why does January 1st always seem to fall on Saturday 7 years after any year it falls on Thursday?
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