January - Math Puzzles
By: Xavier Blackwell-Lipkind
Note: The problems below, listed in no particular order, represent a wide range of difficulties. All, except for problem 1, are original. Watch out for trick questions!
1. What is i^i?
2. How many prime numbers have prime squares?
3. How many numbers have whole-number second and fourth roots?
4. Which is larger: 2^100 or 100^2? Can you find a rule for when a^b is larger than b^a?
5. If you select a random number between 0 and 1, what is the probability that a second randomly selected number is greater than the first?
6. 10% of 10% of x is equal to 51% of x minus 20. Find x.