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.

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