Same Face
A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?
Age
11 to 14
Challenge level
Problem
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The cube occupies positions 1, 2, 3, 4, 5, 6 and 7 in that order, as shown.
Which two of these positions had the same face of the cube touching them on the surface?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
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Then, 1 attaches to the base of the cube, 2 attaches to the right hand face and 3 attaches to the top. 4 attaches to the back face and 5 to the left hand face. 6 then attaches to the bottom face and 7 to the front face.
This means both 1 and 6 are on the same face, so the same face of the cube rolls onto 1 and 6.