# Cubes and Rectangles | Math Olympiad Hanoi 2018

## Cubes and Rectangles - Math Olympiad Hanoi 2018

Try this beautiful problem from Math Olympiad Hanoi, 2018 based on Cubes and Rectangles.

Find the number of rectangles can be formed by the vertices of a cube.

• 6
• 8
• 18
• 12

### Key Concepts

Geometry

Permutation

Combination

Geometry Vol I to IV by Hall and Stevens

## Try with Hints

First hint

There are 6 squares on 6 faces on the cube.

Second Hint

There are 4 diagonals of the cube that have the same length

and pass through the center of the cube. Every two diagonals intersect at the midpoint and form a rectangle.

Final Step

Then there are 6+ $(\frac{4!}{2!2!})$ =12 rectangles.

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