This is a wonderful puzzle contributed by Alok Mittal, through his Maths Circles class.
There is one great minaret in Samarra, but what if the Caliph decided to build twelve? Since the Caliph loves regular geometry, he decides to build those in rotational symmetry on the following grid.
However, he also wants to make sure that every minaret is visible from every other minaret. So the following doesn’t work.
Can you build the twelve minarets of Samarra?
As always, please send your answers as comments within the blog (preferred), or send an e-mail to email@example.com. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.
Happy Minaret Building!