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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?


Please email your answers to deputy-director[at][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.  

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

> 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