skip to content
 

Summer Maths Puzzles - Thursday 8 August - 8 Octopuses

This puzzle, also taken from the first part from one of IBM’s Ponder This collection, seemed particularly apt for today.

An octopus has 8 arms which we can number from 1 to 8. 

We have eight octopuses named A,B,C,D,E,F,G and H.  Each octopus has a watch on each of its arms set to the times shown below.  These are special watches which show only the hour. 

  • Octopus A's watches on its 8 arms numbered 1..8 are set to 1, 2, 3, 4, 5, 6, 7 and 8 respectively.
  • Octopus B's watches on its 8 arms numbered 1..8 are set to 2, 4, 6, 8, 10, 12, 2 and 4 respectively.
  • October C's watches on its 8 arms numbered 1..8 are set to 3, 6, 9, 12, 3, 6, 9 and 12 respectively.
  • Octopus D's watches on its 8 arms numbered 1..8 are set to 4, 8, 12, 4, 8, 12, 4, 8 and 12 respectively.
  • Octopus E's watches on its 8 arms numbered 1..8 are set to 5, 10, 3, 8, 1, 6, 11 and 4 respectively.
  • ...and so on....

To adjust the hour on the watches, we can move all the watches of a single octopus (octopus C for example) one hour ahead, or move all the watches on a specific arm of all the octopuses (arm #3 for example) one hour ahead.

What adjustments do you need to make to fix it so that over 2/3 of the 64 watches show either 3, 6, 9 or 12?

 

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. 

> 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