The only numbers whose only prime factor is 2 are the powers of 2, of the form 2n. I think I'm probably not understanding the problem, though, because the second problem seems to allow only {1,2,3,6}, and no other solutions. Maybe your friend meant "not divisible by primes that are not 2 or 3?" (Also, you friend is guilty of clumsy wording with too many "not's". Try "... only divisible by (primes?) 2 or 3."

What is this for? Is this a homework question or just idle curiosity? Please be honest. If it's for homework I won't tell you the answer outright, but I'll put a lot more effort into helping you understand why it's the answer.

Alright then. As it turns out l = S. I solved it by plugging the givens into a CAD programms and letting it figure out the rest. Doing it by hand is possible but much more complicated.

There are 12 chromatic pitches. If you go in quints (7 chromatic pitches at a time) 7 and 12 have greatest common divisor 1, so you cycle through all pitches. But a third has 3 respectively 4 steps. Both numbers divide 12 (in particular don't have GCD 1 with 12) so you do not cycle through all of them. That's modular arithmetic.

What is the reasoning?

Never mind! I have it

The only numbers whose only prime factor is 2 are the powers of 2, of the form 2n. I think I'm probably not understanding the problem, though, because the second problem seems to allow only {1,2,3,6}, and no other solutions. Maybe your friend meant "not divisible by primes that are not 2 or 3?" (Also, you friend is guilty of clumsy wording with too many "not's". Try "... only divisible by (primes?) 2 or 3."

Hehe yes I was confused about this too. I’ll double check the meaning

Have you tried writing down any numbers that meet these requirements?

Great idea. I’ll work on this

What is this for? Is this a homework question or just idle curiosity? Please be honest. If it's for homework I won't tell you the answer outright, but I'll put a lot more effort into helping you understand why it's the answer.

Hi! It’s a curiosity problem. Thank you for checking

Alright then. As it turns out l = S. I solved it by plugging the givens into a CAD programms and letting it figure out the rest. Doing it by hand is possible but much more complicated.

Do you know how to start doing it?

Sorry, but I dont think this is correct.

Exactly this! Thank you for explaining so well

We also know that AK=CK and therefore AKC is a triangle with at least 2 sides equal and the base equal to S.

Yes. Using symmetry is really useful

If the kink is exactly in between A and B, re draw the picture to be a little more accurate.

Oooh perfect! Thank you

There are 12 chromatic pitches. If you go in quints (7 chromatic pitches at a time) 7 and 12 have greatest common divisor 1, so you cycle through all pitches. But a third has 3 respectively 4 steps. Both numbers divide 12 (in particular don't have GCD 1 with 12) so you do not cycle through all of them. That's modular arithmetic.

Thank you!!