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'Inky Cube' printed from http://nrich.maths.org/

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What do you know about the faces of the cube?
How will you remember what you have done so far?
How will you try to find a route that works?
How do you know you have found all the possible routes?
How will you check that your route/s definitely work/s?
 
Don't forget that each face of the cube is different.