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Math Prize 2021 Problem 18

Source:

September 19, 2021
Math Prize for Girls

Problem Statement

Let NN be the set of square-free positive integers less than or equal to 50. (A square-free number is an integer that is not divisible by a perfect square bigger than 1.) How many 3-element subsets SS of NN are there such that the greatest common divisor of all 3 numbers in SS is 1, but no pair of numbers in SS is relatively prime?
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