1. 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."

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

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

  4. 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.

  5. 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.

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

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

  8. 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.

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