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Sociable Cards

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources


Sociable Cards printable sheet
 

Take a pack of cards and remove the Jacks, Queens and Kings.
Shuffle the remaining cards, and then lay the whole pack face up on the table in a snake, like this one:
 
snake of cards
 
Place four different coloured counters on the first four cards in the snake. Then move each counter foward the number shown on its card (Aces count as $1$). Keep moving each counter until it can't go any further without going off the end. 

Watch the video below to see a demonstration:

Did your counters all finish on different cards?
Repeat the experiment a few times.
How often did all the counters finish on different cards?
How often did they all finish on the same card?
Can you explain your results?
 
Challenge
Find a way to arrange the cards so that all four counters finish on different cards.
Can you do the same with five counters?
 
This problem is based on a card trick called Kruskal's Count
 
 

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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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