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Challenge 240: Rubik's routes

These two problems are both about a cube, each face of which is divided into 9 small squares (like a Rubik’s cube).

a Is it possible to draw a continuous path on the cube which visits each small square exactly once, and returns to its starting point? The path must cross from one small square to another across the middle of an edge of the square, not at one of its vertices.

Explain your answer clearly.

b Is it possible to draw a continuous path on the cube which crosses each small square exactly once along a diagonal from one vertex to the opposite vertex, and returns to its starting point?

Explain your answer clearly.

 

Submit your solution

Please do send in your solution to this problem to  weeklymaths@kcl.ac.uk  You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide you with feedback on your solution.

 

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