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Summer Maths Puzzles - Wednesday 7 August - Encoding Game

Encoding Game

IBM has been setting its challenging Ponder This puzzles every month since 1998.  Up until 2005 these puzzles were set by cryptographer and mathematician Puzzle Master Don Coppersmith.  This is the first part of a puzzle from that era:

A game has the following rules.

  • There are three participants: a Host, a Partner, and a Volunteer.
  • The Partner is in a soundproof room.
  • The Host gives the Volunteer six blank cards, five white and one blue.
  • The Volunteer writes a different integer from 1 to 125 on each card, as the Host is watching.
  • The Volunteer keeps the blue card.
  • The Host arranges the five white cards in some order and passes them to the Partner.
  • The Partner then announces the number on the blue card.

How does the Host use the white cards alone to communicate the number on the blue card to the Partner?

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

  • Cerulean O'Toole
  • Ben Xiao
  • Ben Katz
  • Lindsay Woodhead
  • Soham Sud
  • Richard Hibbs
  • Iam Paczek


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