Problem of the Week #60: Monday August 26th, 2024
As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems.
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This problem is inspired by this twitter post.
Here’s a way to put 6 dots into a 3×3 grid such that no 3 dots form a straight line.
a). Find a way to put 8 dots into a 4×4 grid such that no 3 dots form a straight line.
b). How many ways are there to put 8 dots into a 4×4 grid such that no 3 dots form a straight line?
c). Is it possible to put 10 dots into a 5×5 grid such that no 3 dots form a straight line?
d). Is it always possible to put 2n dots into an nxn grid such that no 3 dots form a straight line?
e). How many dots can we fit into a 3x3x3 cube such that no 3 dots form a straight line?
f). How many dots can we fit into an nxnxn cube such that no 3 dots form a straight line?
g). Share your own problem inspired by this one.
h). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.