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Summer Maths Puzzles - Monday 12 August - Martian Birthday Paradox

Martian Birthday Paradox

The oldest child, who wants to be an astronaut, remains obsessed with all things relating to Mars and this inspires the parents for today's challenge.  

The Birthday Paradox, the parents explain, famously asks what is the smallest number of people that you need in order for the probability of two of them sharing a birthday to be greater than 50%.   The surprising answer to this question is 23. 

[If you haven’t seen this problem before then read up about it online or watch a video tutorial - see eg https://www.youtube.com/watch?v=KtT_cgMzHx8].

The parents tell the children first to go and research how many days there are in a Martian Year and then to calculate how many Martians there would have to be at a party to make it more likely than not that two of them share a birthday?

Help the children solve this challenge.  Their reward will be to go to visit the planetarium.  

For fun, since you know the answer to the regular Birthday Paradox, why not try estimating the answer for the Martian Birthday Paradox before you do your calculation.

Bonus question for which we don't know the answer: is reality consistent with the statistics?  Given that 23 people is equivalent to a referee and 2 teams of 11 football players each, did at least two people share a birthday for over half the Premier League games last season?

 

Please email your answers to deputy-director[at]newton.ac[dot]uk and remember to include your name (or the name of the group that you solved the puzzle with) so that we can publish it on our website if you are one of the first few to successfully solve the problem.  Please be aware that until Monday 19 August replies to each submission may be slightly delayed due to INI staff annual leave, but do be reassured that each message is read and greatly appreciated.    

Answers to all puzzles will be published at the end of the month. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons