Knight's swap
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Age
7 to 11
Challenge level
Problem
Swap the stars with the moons, using only knights' moves (as on a chess board).
What's the smallest number of moves possible? (Only once piece can occupy a single square at a time.)
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Getting Started
You might like to draw a square and use some counters to help you
see the moves.
How will you record what you've done?
How will you record what you've done?
Student Solutions
Several people decided that 16 moves were needed to swap the
stars and moons. The really interesting part is the ways they
invented to tell us what the moves were ...
Joshua (Brooklands
Primary School, Suffolk) numbered the squares 1 to 9 like this:
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He says, "I could do the swap of the moons and stars in 16 moves:
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Thomas (Tattingstone School, UK) used the game-board like a map grid.
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Jaimee (Tattingstone School, UK) gave each square a letter and called the Stars S1 and S2, and the Moons M1 and M2.
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Teachers' Resources
Why do this problem?
This problem requires children to make use of visualisation and
to develop their own methods of recording.
Key questions
Do you know how a knight moves in chess?
What could you try first?
How will you record the moves?
Possible extension
Suggest to learners that you can now put the two stars on the
board anywhere except the middle square. Can they find a way to put
them on so that it is impossible to switch the pieces? Can they
give a really clear explanation?
Possible support
Pupils might like to draw a square and use some counters to
help them see the moves.