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The Tour De Clochemerle

Age 14 to 18
Challenge Level Yellow star
  • Problem
  • Getting Started
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It might help to draw a table to show the riders, and their scores at each stage of the race.

    A     B     C     D     E  
  Stage 1           
 Stage 2          
 Stage 3          
 Stage 4          
 Stage 5          
 Total score           

You can then use the information given in the question to start to fill in some of the cells of the table.

It might also help to work out the total score of all five riders.

There is a lot of information in the question, so be prepared to go back and read it again to see if you have missed anything, or if there is some piece of information that you couldn't use initially which you can use later on.

 

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How many numbers are there less than $n$ which have no common factors with $n$?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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