Find the maximum possible number of intersection points between the diagonals of a 13-gon.
Every two hours, a ferry leaves Froopaloop Island and heads due east to the mainland, taking exactly one hour. Then it leaves the mainland and heads due west back to the island, again taking exactly one hour. Then it repeats
Instead of taking the ferry to Froopaloop Island, Heather prefers to do something very risky: she dons her
gorgeous white bikini and swims to the island. (The inhabitants of the island don't know what she looks like with
clothes on.)
One day, Heather left the mainland terminal at exactly the same time the
ferry left the island terminal. Exactly
50 minutes later, the ferry passed her.
Assuming both Heather and the ferry travel at a constant speed, and ignoring the time the ferry spends at the mainland terminal, how much time passed between the ferry passing Heather in the opposite direction and passing her in the same
direction?
Hint: Fifty minutes after leaving the island terminal, the ferry will go in the opposite direction of Heather.
A, B, C, and D represent four different digits that can be combined to yield 24 different four-digit integers.
These 24 integers have the following
properties:
- 4 are primes.
- 7 are the products of two different
odd primes.
- 1 is the square of a prime.
- 8 are divisible by 2 but not by 4.
- 2 are divisible by 4 but not by 8.
- 1 is divisible by 8 but not by 16
- 1 is divisible by 16.
Determine the values of A, B, C, and
D.
