Minarets in the utopian downtown of New Istanbul will be so beautiful that it will be the law that from every minaret, every other minaret may be seen. When the downtown was small this was relatively easy. The following shows 6 minarets in a downtown of 3x3 blocks:

However, it becomes more difficult to construct minarets in a larger downtown. Below a mistake has been made because a person on top of the green minaret cannot see either of the red minarets:

There are two utopian solutions for placing 8 minarets when the downtown grows to 4x4. Can you find both of them?

Extensions:

What is the maximum number of minarets you can place in an NxN utopian downtown?

How many minarets can you place in a 5x5 utopian downtown?

There are two solutions for placing 12 minarets in a 6x6 utopian downtown. Part of each has been completed below:

There are two ways to build 20 minarets in a 10x10 utopian downtown. Complete the second downtown:

Is there any limit to the size of a utopian downtown if its NxN blocks must contain 2N minarets? Warning: This is an unsolved problem in mathematics.

Credits:

This is a classic problem.

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