# Relatively prime numbers

Can you fill in the circles with numbers such that:

• Each pair of circles connected by one line contains relatively prime numbers
• Each pair of circles connected by two lines do not contain relatively prime numbers
• You use one of every element from this set: $$\lbrace 20,21,22,23,24,25,27,28,30,32,33,35 \rbrace$$.

A Relatively Prime Number Set is a collection of integers in which each pair of numbers is coprime, meaning they share no common factors other than 1 (e.g. $$\lbrace9, 3, 1\rbrace$$, $$\lbrace10, 5, 2, 1\rbrace$$, etc.).

Source is from https://brainly.com/question/40900166

• I'm not exactly sure what you mean with the example sets there. $\{9,3,1\}$ is not a set of pairwise co-prime numbers, since the gcd of $9$ and $3$ is $3 \neq 1$. On the other hand, if you meant just that the gcd of all numbers in the set is $1$, then that's trivially true for any set that contains $1$ itself. But do we even care about multi-number sets of co-primes for the puzzle, if it's enough for each pair (connected by one line) to be individually co-prime? Nov 28, 2023 at 15:15
• Me too, somebody decided to edit my question for some reason Nov 28, 2023 at 16:07
• This is too late but this problem was cheating on USAMTS round 2. Discussion is allowed now. Nov 29, 2023 at 15:51
• oh, i did not nkow this Dec 3, 2023 at 20:15