skip to content

Summer Maths Puzzles - Tuesday 6 August - Square Pegs in Round Holes

Square Pegs in Round Holes

As the kids are taking down their tent they strike up a philosophical conversation about square pegs in round holes and thence round pegs in square holes.  They ask their parents the following question:

Which fits better: a square peg in a round hole or a round peg in a square hole?

Can you help the parents solve this problem?  Consider a square inscribed within a circle and circle inscribed within a square as illustrated below.  In each case, find the area of the shaded section as a percentage of the whole.



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

  • Niall and Jenny
  • Ali Raad
  • Veera
  • Krishi
  • Sarisha
  • Evgeny Mirkes
  • Nora Howie
  • Georges Sabback
  • Patrick Luo
  • Austin and Knobloch families
  • Emily Lies, Jan Ricken and Tobias Beyer
  • Soham Sud
  • Sittichoke Som-am
  • Lindsay Woodhead
  • Meg North
  • Ben Katz

> Click here to return to the Summer Maths Puzzles homepage.

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