Here are a couple to ponder. I've got answers (as well as the inevitable pedagogical discussions) over at You Do the Math.
1. If a perfect square isn't divisible by three, then it's always one more than a multiple off three, never one less. Can you see why?
2. Given the following
A B D _______________________________________________
C E F G
Where does the 'H' go?
Infinite primes via Fibonacci numbers
22 minutes ago