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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?

## 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?
If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVI,
puzzles about perfect numbers, or a random puzzle.
© Matthew Scroggs 2018