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In the Bag

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
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Ten marbles of varying colours are chosen at random and placed in a bag.
Can you guess the colours of the 10 marbles in the bag?

To help you make accurate predictions you can choose to see the results of 10 viewings - each viewing removes a marble out of the bag, records its colour and returns it to the bag before repeating the process.

You can choose to perform as many 10 random viewings as you like before deciding to "Guess".
Each Round concludes when you have made a guess.
 


Can you reach a score of 1000 points?

You start with 500 points. Each run of 10 viewings "costs" you 10 points but you can "earn" points by predicting accurately the contents of the bag:

150 points for a perfect match
100 points for 9 matching marbles
0 points for 8 matching marbles
-150 points for 7 or fewer matching marbles.
Can you develop an effective strategy for reaching 1000 points?

Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Describe your strategies.

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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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