Here's a question, what is the maximum amount of arrows that you can draw on the chessboard. It doesn't matter what color you use because a green arrow overlapping a red arrow will have the same effect as a green arrow overlapping a green arrow. Remember that if a1 connects to a2, then a2 cannot connect to a1 because they will cancel each other out.
Such a thing is called a directed graph, or quiver.
If I understand what you're asking, it's 2016.
a1 connects to a2 through h8 (63 connections)
a2 connects to a3 through h8 (62 connections)
...
total = 63 + 62 + ... + 1 = 64*63/2 = 2016.
a1 connects to a2 through h8 (63 connections)
a2 connects to a3 through h8 (62 connections)
...
total = 63 + 62 + ... + 1 = 64*63/2 = 2016.
this is a really basic basic math exercise... i hope no one gets it wrong
He might have meant to count only the arrows that could represent legal chess moves, which would be a little more work.
I'm also concerned with whether arrows that overlap are counted separately. For example we have a1->a2 a2->a3 and a1->a3 together does a1->a3 count since it overlaps with the first two.
If we only accept those that represent legal chess moves, we can count how many squares a piece can move to from any particular square, sum up and divide the answer by 2.
Yes somehow, but (for example) not all squares have the same number of legal moves for each piece or pawn, e.g. a knight can move to 8 squares from the 16 central squares, but only to two from the corners.
Either way it really is just a counting problem ...
Alright i'll create a new thread for a more difficult "counting" challenge. It'll be a bit harder to validate the answer for this one though.
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