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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].

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?

Entry to this puzzle is now closed.  Congratulations to the following for some great answers: 

  • Evgeny Mirkes
  • Fin Scott
  • Lindsay Woodhead
  • Nora Howie
  • Krishi (Kanha Seksaria)
  • Soham Sud
  • Ali Raad
  • Georges Sabback
  • Emily Lies and Jan Ricken
  • Akshay Sant
  • Niall Moran and Jenny McSharry
  • Patrick Luo
  • Ben Katz


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