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I have been asked this puzzle in an interview. There was not a lot of time left so I couldn't solve it quickly and the interviewer kind of let it go as he had to wrap up the interview

Foo and Bar are twin brothers. Foo is older than Bar by 5 minutes. Foo celebrates his birthday every year on March 16th and Bar celebrates his birthday on March 15th. Explain the scenario.

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    $\begingroup$ Why isn't "Foo was born at 12:03 AM and Bar was born at 11:58 PM" a solution? Is there a typo? $\endgroup$ – Milo Brandt Feb 12 '15 at 4:15
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    $\begingroup$ @Meelo - since Foo is 5 minutes older than Bar, Foo would have had to have been born 5 minutes before Bar. $\endgroup$ – Johnny Feb 12 '15 at 5:24
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    $\begingroup$ @Meelo I thought the same thing, at first; on a closer read it's clear that the older brother has the later birthday. $\endgroup$ – Shokhet Feb 12 '15 at 17:00
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    $\begingroup$ The question is protected, so I can't answer, and will instead comment here (spoiler): the younger brother lives in (for example) China, and the older brother Iives in (for example) the U.S.; thus, without any oddity surrounding their birth, the younger brother celebrates their birthday a day early (a simpler use of timezones than any proposals thus far). $\endgroup$ – michael Feb 14 '15 at 13:17
  • $\begingroup$ It could be that they were both born on the 15th (or 16th) and fought for birthday attention so decided (for various possible reasons) to celebrate that way. (I'm exploiting the fact that you only specified when each "celebrates".) $\endgroup$ – Quinn Culver Mar 10 '15 at 4:43

16 Answers 16

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Foo is older than Bar, but celebrates his birthday the day after Bar because one of the following happened:

1. The mother was on a boat or a plane traveling eastward. Foo was born on March 16th, then the boat/plane crossed the International Date Line, and 5 minutes later, Bar was born on March 15th.

2. The mother was traveling westward between 12am and 1am. Foo was born on March 16th, then they crossed a time zone, and 5 minutes later, Bar was born on March 15th. (This was mentioned in dmg's comment).

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    $\begingroup$ If they were about to celebrate their 21st birthdays, then they would be old enough to have been born on land. Until Jan 1st 1995, the IDL used to pass through the Republic of Kiribati and also Taveuni Island in Fiji. In principle that means they could have been born on opposite sides of an appropriately positioned bed. Less likely, they could also have been born on Antarctica, or on arctic sea-ice. $\endgroup$ – Penguino Feb 12 '15 at 3:45
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    $\begingroup$ Yeah, I was getting ready to answer Daylight Savings Time, but that is impractical because 1) the summer months move forward in the hour, not backward, and thus we'd have to assume they were born south of the Equator; and 2) even if the hour did get pushed back, it wouldn't get pushed back to the day before DST is no longer observed, i.e. the rollback happens on the hour and the date doesn't change. I thought I'd share this, in case it was the answer Vallabh was looking for. $\endgroup$ – Bulldogg6404 Feb 12 '15 at 5:55
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    $\begingroup$ you were faster than me by a mere 8 hours :( $\endgroup$ – Novarg Feb 12 '15 at 8:41
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    $\begingroup$ It will work with any timezone, not only the IDL. $\endgroup$ – buffo Feb 12 '15 at 9:49
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    $\begingroup$ It's also possible that the mother stayed in the same place but the timezone changed - not as in daylight savings time, but rather political changes, as in the case of Samoa's recent jump from one timezone to another (although it would need to be in the opposite direction to that example of course - but it's happened in other places too, China and Russia spring to mind). $\endgroup$ – A E Feb 12 '15 at 20:23
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Because they are...

... identical twins, although this isn't a necessary requirement for this answer, it can come in handy.

And they were born...

... before and after midnight

And...

... their identities got mixed up, i.e. the parents think they named their oldest twin Bar and act accordingly.

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  • $\begingroup$ +1 Interviewers often look for the simplest answers. This one is simpler than the time zone answer. $\endgroup$ – nhaarman Feb 12 '15 at 22:08
  • $\begingroup$ This is often overlooked and far and away the simplest answer! $\endgroup$ – Yablargo Feb 13 '15 at 15:59
  • $\begingroup$ That's pretty clever. $\endgroup$ – smci Feb 14 '15 at 0:06
  • $\begingroup$ @KNU Stack Exchange has a strict "Be Nice" policy. Please remember to abide by it. $\endgroup$ – Doorknob Mar 30 '15 at 12:21
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Here's an answer suggesting human error,

They were born on either side of midnight, but the birth certificate guy got it backwards!

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    $\begingroup$ This is the most likely explanation in real life. $\endgroup$ – Florian F Feb 12 '15 at 21:21
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    $\begingroup$ On a similar bureaucratic level: although I was born before my twin, for the purposes of the social security benefits given to our parents she was the one who officially received the slightly larger payment for the eldest child. Why? Her name comes before mine alphabetically. $\endgroup$ – Peter Taylor Sep 18 '15 at 19:13
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I honestly think that the simplest answer is that

Foo and Bar are both twins, but not twinned to each other. In fact, they aren't related to each other at all.

Which means that

Foo and his twin brother Baz could celebrate their birthdays on the 16th in Australia. Bar and his twin brother Qux were born 5 minutes later (but in the UK) meaning that their birthdays are on the 15th.

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  • $\begingroup$ This sounds more legit for an interview question. $\endgroup$ – Rohinb97 Feb 15 '15 at 9:12
  • $\begingroup$ It reminded me of the sort of word-play you find in quite a lot of brainteasers; e.g. The ship had three people on board when it sank. Every single person drowned but there was only one funeral, why? Because two of the people were married, not single. $\endgroup$ – Richard Feb 15 '15 at 9:13
  • $\begingroup$ ^That could be a nice question! $\endgroup$ – Rohinb97 Feb 15 '15 at 11:10
  • $\begingroup$ @Rohinb97 - Based on what I've seen over the last few month, open-ended brainteasers aren't really welcome here. $\endgroup$ – Richard Feb 15 '15 at 11:13
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It's simple. It's not about strange time-zone scenarios, however they may be possible. The interviewer probably wanted to test if you can think outside of the 'nerd' box.

They were simply born at almost the same time. To not have to celebrate the birthday on the same day, which may not be much fun for either of the kids, the parents decided to celebrate the birthdays on separate days. They didn't care about the 5 minutes, or maybe didn't even want to tell the kids which one was first, to treat them equally. In the end, this became a tradition they kept.

That, is by far a more likely scenario than any weird 'traveling with enormous speed' scenario.

This is the whole point of interviews. You have to discover on what modes and levels people can think.

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Because semanthics:

Foo celebrates his (brother's) birthday every year on March 16th and Bar celebrates his (brother's) birthday on March 15th. Celebrating my brother's birthday.

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  • $\begingroup$ It'd be nice to know why the down vote. I honestly believe it's the same type of solution as the one for the Poisoned Iced Tea puzzle (and it doesn't even need the strain of accepting the idiom "poisoned iced" as meaning "poisoned ice") $\endgroup$ – Shivan Dragon Feb 12 '15 at 14:33
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    $\begingroup$ I like this - because semantics are a HUGE part of many puzzles like this and in some aspects makes perfect sense. I want to agree with it... but after some thought and some rewording: Jack is born on the 15th, John on the 16th. Jack celebrates Johns birthday on the 15th. John celebrates Jacks birthday on the 16th just doesn't "connect" for me. I've never heard of brothers celebrating the others birthday on their birthday, unless that's a local custom type thing... $\endgroup$ – WernerCD Feb 12 '15 at 17:10
  • $\begingroup$ this is a lot more likely than the timezones answer imo. $\endgroup$ – user3453281 Feb 12 '15 at 17:25
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    $\begingroup$ @ShivanDragon While we can stretch "semantics" so that "Foo celebrates his birthday" means "Foo celebrates his BROTHER'S birthday" I don't see how you can stretch it even more to reverse the meaning of "his" in the next sentence. So no, this one contradicts the statement of the problem. As for "Poisoned Iced Tea" puzzle the answer is perfectly normal in my view not requiring "semantics" or idioms ("poisoned iced tea" means drink called "iced tea" that is poisoned). $\endgroup$ – Incassator Feb 12 '15 at 23:10
  • $\begingroup$ Agreed, my solution is sort of stretchy. But I honestly feel that the other answers offer rather stretchy solutions as well. Maybe the puzzle doesn't have an elegant solution. $\endgroup$ – Shivan Dragon Feb 13 '15 at 9:41
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Fairly sure @pacoverflow had the answer you wanted, but here's an alternative solution:

Foo and Bar are non-identical twins. If you measure their relative age from conception, then it is plausible that Foo was conceived 5 minutes earlier, but was actually born an hour or so later (on the other side of midnight, clearly) from Bar.

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  • $\begingroup$ FWIW "non-identical" twins are generally referred to as "fraternal" twins. $\endgroup$ – The Guy with The Hat Feb 14 '15 at 15:26
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    $\begingroup$ Who ever measures age from conception? $\endgroup$ – David Richerby Feb 14 '15 at 17:33
  • $\begingroup$ @DavidRicherby Age from conception is sometimes used when evaluating premature children relative to full-term children on physical and intellectual development. A 36-month-old child who was born 2 months premature might be compared to 34-month-old full term child. $\endgroup$ – Ellen Spertus Feb 15 '15 at 1:53
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This, I believe, is a less far-fetched scenario than the intended answer.

Foo and Bar were adopted as babies by different families. They were born orphans. The orphanage was worried nobody would want to adopt two children at a time, or that it would bring less money, so they falsified one birth certificate and changed the date.

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Bar may have been older than Foo at the time of birth, but then became an astronaut and has been participating in tests of new propulsion technologies, while Foo had a regular job (which did not involve that kind of acceleration Bar was frequently experiencing).

Now due to effects of time dilation Foo is actually 5 minutes older than Bar, despite celebrating his birthday after Bar's

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One Solution could be

The woman is native of the Yoruba nigerian tribe which belives the older twin is the second born. Then the oldest twin by 5 five minutes is the second born by 5 minutes. Hence Foo was simply born at 12:03 AM and Bar was born at 11:58 PM.

Based on

The first born twin, whether a boy or a girl, is always called Taiwo, meaning `having the first taste of the world’, whereas the second is named Kehinde, meaning ‘arriving after the other’. Although being born first Taiwo is considered as the younger twin.

Additionally

This belief is held in many african tribes, and I did hear it once as a tradition in France although it is not the case officially (this is how I got this idea). I'm pretty sure we can find other culture that hold that belief?

here is some links

Yoruba, Northern Ivory Coast

This is kind of far-fetched, probably not what interviewer would be looking for but this work :).

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I think the emphasis on other answers has been in solving the abstract puzzle that was presented (which is very reasonable on this forum). In an interview situation, if you were able to come up with these different possible explanations, then selecting the "best" explanation (assuming you get one chance to answer) would probably depend on the nature of the interview.

The time zone answer is an appropriate choice for any company which engages in business across multiple time zones (demonstrates awareness of the issues that time zones can create), and for certain companies it may even earn bonus points if you can point to a specific location where this could have occurred: "Foo was born in X while his parents were travelling towards Z on a boat, Bar was born in Y 5 minutes later" where X Y and Z are locations that the company does business.

The mixup identity answer is the answer I'd go with if I were interviewing for an editorial/newspaper job because it demonstrates a focus on the precise wording of the question ("Foo celebrates his birthday on X" instead of "Foo was born on X")

And finally, if I were interviewing for any position related to a religious organization which defines life as beginning at conception, it would be very hard to go wrong with the conception answer.

Personally mixed up identity is what I believe to be the generic "most likely" answer to this puzzle (in that there probably exist more people who have been born under those circumstances than the time zone answer, and it doesn't require playing with the definition of life), and it seems logical that if the puzzle is worded as "celebrates his birthday on..." there's a reason it didn't simply state "was born on," so if a business doesn't meet any of the criteria above I'd definitely go with mixed-up identity. Even more so if it's a stock analysis or prediction of any kind job where best guesses often have to be relied upon because you cannot know something with certainty.

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They don't have to have been born on either side of the date line. All that is required is for one of the twins to have since moved to the other side of the date line from where they were born. For example they might have been born on the 16th and the younger one is celebrating on the 15th because "it's already the 16th where I was born" or they might have been born on the 15th and the older one is celebrating on the 16th because "it's finally the 15th where I was born."

Alternatively, they don't need to move, just live somewhere that has moved to the other side of the dateline, such as Samoa, and one of them use the calendar date of their birth even though the country skipped a day in the switch, and the other insist on waiting a day until the birthday is truly reached. One of my children corrected any "Happy Birthday"s that were given before the time of day of the birth, saying "I haven't turned [whatever] yet" until that time rolled around. I can see a similar approach applying in a dateline switch situation.

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My first post here.

Foo and Bar were both born on the 15th.

Bar died on his birthday which results in Foo celebrating his birthday on the 16th of every year. It doesn't state that Bar celebrates his birthday every year.

The key word here is 'celebrates'.

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  • $\begingroup$ Hmmm, then how can Bar celebrate on the 15th? $\endgroup$ – Len Feb 12 '15 at 20:15
  • $\begingroup$ It doesn't state that Bar celebrates his birthday every year. $\endgroup$ – Booleanz Feb 12 '15 at 20:16
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    $\begingroup$ If Bar died, then "celebrated" would have been used. $\endgroup$ – Len Feb 12 '15 at 20:18
  • $\begingroup$ I guess so, unless the date of his own death was known beforehand. $\endgroup$ – Booleanz Feb 12 '15 at 20:30
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Bar was positioned within his mother's womb to be born first. Foo was positioned in his mother's womb to be born second. Due to complications, a caesarian had to be performed in order to safely bring the twins into the world. Foo was removed from the womb first, Bar was removed 5 minutes later. Because of time honored tradition, the parents wanted the birthdays to be celebrated in the "naturally intended" order. Therefore, Bar's birth is celebrated on March 15th and Foo's on the 16th.

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Another pair of (related) potential solutions:

Foo moved to a country that has a National Holiday on March 15th (Hungary, for example). So his birthday is not overshadowed, he celebrates it on the 16th, the next day.

Similarly but differently:

Bar converted to an obscure religion with a practice that requires him to celebrate his birthday the day before. Perhaps the religion advocates celebrating when your mother went into labor, not the time of the actual birth. Or the religion does not acknowledge time zones; time, regardless of where you are on Earth is based on the time of the central temple. When Bar converted, he began to adhere to that, thus adjusted the time zone of his birthday, making it the day before.

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Both brothers were born just before midnight on the 15th; however, unfortunately Foo was non-responsive at birth but was revived just after midnight.

Even though Foo was out of the womb first, he celebrates his first breath of life which happened after the date change.

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protected by Aza Feb 13 '15 at 10:36

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