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Calendars can repeat after either 5 years, 6 years or 11 years. So if there is a repetition after 6 years and again after 11 years, that will be at total of 17 years. 2005 repeated in 2011, 6 years later, and will repeat 11 years after that in 2022. 2006 will repeat in 2017, 11 years later, and in 2023, 6 years after that.

The pattern is down to the way leap years affect the day a year starts. Obviously there are 7 days in a week. In a 7 year period there is either one or two leap years, so either one or two days will be skipped. If one day is skipped, then the same day can come around again in 6 years. If two days are skipped a day can come around in 5 years. However, for the day that is actually skipped, it will take it longer to come around, and that is why it can be 11 years. Also if a leap year occurs, it will have an extra day so the calendar will be different.

2006 started on a Sunday. 2012 also started on a Sunday, but it was a leap year, so there was an extra day, instead of the 365 days that 2006 had. 2012 and 2016 are both leap years. If you look through the full list from 2005 to 2023, you will see the patterns. If you take any day of the week a year starts on and the other years that also start on the same day, you will see there is that 5, 6 or 11 year gap:

Saturday 1 January 2005

Sunday 1 January 2006

Monday 1 January 2007

Tuesday 1 January 2008 (leap year)

Thursday 1 January 2009

Friday 1 January 2010

Saturday 1 January 2011

Sunday 1 January 2012 (leap year)

Tuesday 1 January 2013

Wednesday 1 January 2014

Thursday 1 January 2015

Friday 1 January 2016 (leap year)

Sunday 1 January 2017

Monday 1 January 2018

Tuesday 1 January 2019

Wednesday 1 January 2020 (leap year)

Friday 1 January 2021

Saturday 1 January 2022

Sunday 1 January 2023

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Q: Why do certain calendars repeat after 17 years - 2022 and 2023 will be the same as 2005 and 2006?
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