Question: 1. Prove or give a counterexample: Every multiple of 6 that is greater than or equal to 12 is the sum of two consecutive primes. (For example, 30 = 13+17)
2. (Adapted from [10]) Figure shows a network of canals around artificial islands in a pond, created as a duck playground. White Duck (pictured in Figure A.10) swims aimlessly around the playground and then goes to see Grey Duck. White Duck says, "I swam through each of the 16 canal intersections at the playground exactly twice. In fact, here's the order in which I swam: a-o-n-h-k-g-b-m-i-e-p-f-c-l-d-j-c-g-n-h-j-k-d-l-p- i-e-f-b-o-a-m." "The canal intersections aren't usually labeled," replies Grey Duck, "so I don't exactly know the path you took. But you know what? I think you can't be quite right about where you swam." White Duck pauses to think, then responds, "Ah, yes, you're right. I switched two of the letters in my order." Can you figure out what White Duck's error was?
