Problem of the Week #92: Monday June 16th, 2025
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 the 1974 Canadian Math Olympiad Q4.
a). If we place 3 points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
b). If we place 4 points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
c). If we place n points on a line segment of length 1 and add up all pair-wise distances between them, what’s the biggest sum we can get?
d). If we place 4 points on the circumference of a unit circle and add up all pair-wise distances between them, what’s the biggest sum we can get?
e). If we place n points on the circumference of a unit circle and add up all pair-wise distances between them, what’s the biggest sum we can get?
f). If we place 4 points on the perimeter of a unit square and add up all pair-wise distances between them, what’s the biggest sum we can get?
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.