You are waiting for an appointment in the doctor's office and it looks like she is running late. Unfortunately, your iPhone (or Blackberry) battery is out and other than a Fly Fishing Magazine, all are taken. You suddenly become preoccupied with your son's Bar Mitzvah that is still three years ahead, but you need to reserve a place. You are trying to figure out what day of the week his birthday will fall on in 2013. It falls on Thursday this year, 2010. Is it humanly possible to deduce this without a calendar?

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## 6 comments:

I've got an idea of how to do it though I'm not sure it's right. Hopefully others will be able to build on my answer though.

Yes, it is humanly possible to deduce this without a calendar.

If you know that your son's Bar Mitzvah falls on a Thursday, you know that moving 7 days ahead will also be a Thursday.

All you have to figure out then, is how many 'weeks' there are between 2010 and 2013 then calculate the remaining days (if any) and then move ahead from Thursday that many days.

For instance, we know that (that particular Thursday) 2010 - (that particular Thursday) 2011 is 365 days. And then, there's 366 days from 2011 - 2012 (2012 being a leap year). And then finally, another 365 days from 2012 - 2013 (again, all of these going from the Bar Mitvah's Thursday date to the next year's Bar Mitvah's Thursday date.

So in total, there are 365 + 366 + 365 days and to calculate the number of weeks, we divide this total by 7.

1096 / 7 = 156 + 4 days left over.

So there are 156 weeks and then starting from Thursday:

1: Friday

2: Sat

3: Sun

4: Mon

So, if all my math and logic worked out, it should be a Mon in the year 2013.

We should all know, but do not all know, that April Fool's Day (for instance) moves forward in the weekdays each year MTW etc; except in leap years, when it moves ahead TWO weekdays, since April 1 is after Feb 29.

If the birthday is Thursday this year, it'll be on a Friday in 2011. In 2012 which is a leap year, it'll be on a Saturday or a Sunday depending on when the birthday falls (before or after Feb 29). In 2013 it'll be a Monday in any case, and so forth. Tom

Two great explanations!

Wang definitely gets a puzzle point. Tom also deserves one, but can't get it. Two reasons: he was second here and he also already solved another puzzle this week - Hot Pink Gum Balls.

I just want to add that those of us who like me and can't divide (365 + 366 + 365) = 1096 by 7 in their brain without a piece of paper and can't wrote on a Fly Fishing Magazine, can come to Tom's solution by thinking that:

365 days a year is 350 + 15

350 is definitely divisible by 7 as it is half of 700; so whenever you add 350, you end up on the same day of the week

take a loot at 15

it is 14 + 1

add 14 days and you are again on the same day of the week you started with;

so the day shift you have is 1

in a leap year, with 366 days per year, we have a day shift of 2

just like Tom summarized.

Thought it was just common knowledge that whatever day a date is on one year, it's the next day the next year. So his birthday would be on Friday in 2011, Saturday in 2012 and Monday in 2013 because 2012 is a leap year.

If the birthday is on a Thursday in 2010, then the birthday will be on Friday in 2011. Because 2012 is a leap year, one must skip a day, and go to Sunday in 2012, and the child's birthday will fall on Monday in 2013.

2012 is a leap year. A boy having a bar mitzvah in 2013 was likely born in 2000, also a leap year. This means his birthday could be Feb 29, 2000. This raises the question of when the birthday is celebrated in 2010: on Feb 28 or March 1? Let's assume the mom knows this and that the mom is human.

All dates from 2010 advance one weekday in 2011. All dates in 2011 from Jan 1 to Feb 28 advance one day in 2012 and two days in 2013; all dates in 2011 from March 1 till December 31 advance two days in 2012 and 1 day in 2013. The remaining question then is the possibility of the Feb 29, 2000 birthday. The mom will know if her son's birthday is celebrated on Feb 28 or on March 1 of non-leap years such as 2013. So it is possible for her to calculate the weekday of her son's birthday, but for the rest of us, a Feb 29 birthday remains problematic.

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