NOTE:  Newest BTs in red, Bonuses in blue, comments in green, updates in purple.

1. Simplify: (2 + 0 + 2 + 2)² – (2 – 0 – 2 – 2)² + 20 – 22
2. When could it believably be said that 8 + 8 = 4? (Suspect there may be multiple answers?)
3. 9,811,438,761 divided by 9 leaves what remainder?
4. A board 2.5 meters long is divided into ten equal pieces. How long – in centimeters – is each piece?
5. Two different prime numbers are selected at random from among the first ten primes. What is the probability that their sum is 24?  (Express your answer as a fraction.)
6. Too easy? Merry Christmas!  😊  
7. Find the least common multiple of 10, 15, and 18.
8. How many distinct rearrangements are there of the word “MATH”?
9. You have 628 cm. of string, which you may form into either a square or a circle. Which figure will yield the most area?
10. The maximum speed of a zebra is 40 mph. IF the zebra could keep up that speed, how long would it take it to run one mile?
11. How many positive integers less than 124 are divisible by 2, 3, and 5?
12. Find the product of the first five even whole numbers.
13. Which of the following best describes the GCD of two numbers?  a)  always even  b)  always odd  c)  never prime  d) none of these.
14. There are several combinations of whole numbers whose sum is 12.  Find the pair with the greatest product.
15. Find two examples of numbers that have exactly three factors (no more, no less).
16. 

 
Bonus 1:  See  #3 above.  What slick math tidbit makes this problem easy to solve without paper, pencil, or calculator?
Bonus 2:  Square a two-digit number and subtract one.  Under what conditions will the result be prime?
Bonus 3:  Write the number (12⁴ – 5⁴) as a product of primes.
Bonus 4:  See #15.  Do you know (or can you deduce) what is true in general about integers with exactly three factors?