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Sunday Afternoon Maths LXIII

 Posted on 2018-04-22 

Is it equilateral?

In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.
Is triangle \(ABE\) equilateral? Why/why not?

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Cube multiples

Six different (strictly) positive integers are written on the faces of a cube. The sum of the numbers on any two adjacent faces is a multiple of 6.
What is the smallest possible sum of the six numbers?

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If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,
puzzles about triangles, or a random puzzle.
© Matthew Scroggs 2019