This week my friend Irina complained to me that her son's 17th birthday fell on the Boston Marathon Day and friends weren't able to come and celebrate with them in their Brookline home until the roads opened. Previous such coincidence was 17 years ago when her son Daniel was just born in the Beth Israel Hospital that is right along the marathon route and all the visitors got delayed till the end of the marathon festivities. Irina mused that I could probably calculate when the next such coincidence would happen and I thought why not turn it into a puzzle.

Daniel's birthday is April 21.

Boston Marathon is held on Patriots Day that is 3rd Monday in April.

Is Irina correct that the Boston Marathon coincided with Daniel's birthday only twice: in 1997 when he was born, and now in 2014? When is the next time such a coincidence will happen?

Image from Flickr, distributed under CCL.

Your thoughts and suggestions are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

## 5 comments:

After 1997, April 21st was a Monday in 2003, 2008 and this year, 2014. April 21st is going to be a Monday in 2025,2031,2036,2042 and so on.

Consider a unit to be 4 years. 4 years has 5 days extra, 4 in each year + 1 from a leap year in the 4 years.

5*1unit + 2days makes a week; 4years + 2 years = add 6 => 1997 + 6 = 2003

5*2units + 4days makes 2 weeks; 8years + 3 years = add 11 => 1997+11 = 2008 (leap year!)

5*3units + 6days makes 3 weeks; 12years + 5years = add 17 =>1997 + 17 = 2014

5*4units + 1day makes 3 weeks; 16years + 1year = add 17 =>1997 + 17 = 2014

5*5units + 3days makes 4 weeks; 20years + 3years = add 23 => 1997 + 23 = 2020 NO! because 2020 is a leap year and that adds 4 days and not 3 and the equation fails and 21st is not a Monday.

5*6units + 5days makes 5 weeks; 24years + 4years = add 28 => 1997 + 28 = 2025

5*7units + 0days makes 5 weeks; 28yars = add 28 => 1997 + 28 = 2025

5*8units + 2days makes 6 weeks; 32years + 2years = add 34 => 1997 + 34 = 2031

5*9units + 4days makes 7 weeks; 36 + 3(2036 is a leap) = add 39 => 1997 + 39 = 2036

5*10units + 6days makes 8 weeks; 40years + 5years = add 45 => 1997 + 45 = 2042

Interesting question. The key to it is to have April 1 fall on a Tuesday. The reason you want to do that is because the first Monday of the month is April 7th The next Monday is April 14 and then you get the third Monday as April 21 which is what you want.

Your friend is quite correct. This happens on 1997 and 2014. In between those two years, it also happens on 2003 and 2008. Now here's where things get a little dicey. The next time it happens is on 2025 which I find a bit hard to believe. The other occurrences seem to have a pattern (more or less). This one seems a bit out -- don't ask me why.

Is the answer 2025?

I used open office as my spreadsheet and the date format is 01/04/1997 as cell A1 and b1 is =weekday(a1) which returns a 3 for 1997. Weekday for 2014 returns a 3 and so does 2003 and 2008. I am not totally sure I have not made a mistake in filling the dates in which is why I'm being so detailed.

I think that Daniel's birthday (Apr 21st) was on the 3rd Monday in April two additional times since 1997, in 2003 and 2008. The next year that it will be on a Monday is in 2025.

For each year since 1997, the day of the week for April 21st (or any date except Feb 29th) moves ahead one day except for on a leap year when it moves ahead 2 years.

Day of the week for April 21st:

1997: Mon; 1998: Tues; 1999: Wed; 2000: Fri; 2001: Sat; 2002: Sun;

2003: MON

2004: Wed; 2005: Thurs; 2006: Fri; 2007: Sat;

2008: MON

2009: Tues; 2010: Wed; 2011: Thurs: 2012: Sat; 2013: Sun

2014: MON

2015: Tues; 2016: Thurs: 2017: Fri; 2018: Sat; 2019: Sun;

2020: Tues; 2021: Wed; 2022: Thurs: 2023: Fri; 2024: Sun

2025: MON

TracyZ

The Boston Marathon coincided with Daniel's birthday in 1997, 2003, 2008 and 2014.

The marathon is held on the 3rd Monday of April, if it has to coincide with Daniel's birthday on the 21st, the month of April has to begin on a Tuesday.

Year Day(1st of April)

1997 Tuesday

1998 Wednesday

1999 Thursday

2000 Saturday (leap year)

2001 Sunday

2002 Monday

2003 Tuesday

As the month of April begins on a Tuesday in 2003, the 21st of April of 2003 will be on the 3rd Monday.

The next such coincidence occurs in 2008 and then in 2014, 2025, 2031, 2036 and so on....

Lulu

The bravest have tackled this one. A big fat puzzle point to SN, Jerome, TracyZ and Lulu.

One important thing to remember about the calendars: date moves one spot along the days of week on every year that is not a leap year and two spots on a leap year. That means that if you April 21st is on Monday this year, it will be on Tuesday next year, Thursday in 2016 (leap), Friday in 2017 etc.

I will tell Irina that next coincidence is going to happen in 2025 and that she forgot about 2003 and 2008 (perhaps that was the period they were living in NJ :). Thank you all!

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