1. On a balance scale, three green balls balance six blue balls; two yellow balls balance five blue balls; six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow, and two white balls?

2. In the figure, ABCD is a square and ABE is an equilateral triangle and E is in the interior of ABCD. Find the measure of angle DEA.

3. Find the next term in the sequence: 1, 1, 1, 3, 5, 9, 17, 31, 57, …

4. If log₂(log₃x)=4, find x.

5. In a group of men and women, the average age is 31 years. If the average age of the men is 35 years and the average age of the women is 25 years, what is the ratio of the number of men to the number of women?

6. If a triangle has sides of length 10, 24, and 26, what is the radius of its circumscribed circle?

7. How many positive integer values of x are there such that 96/(x + 5) is an integer?

8. Find the two rightmost digits of 1! + 2! + 3! + ... + 100!.

9. How many ways are there to fill a 3×3 grid with 0’s and 1’s so there is at least one zero in each row and column?

Here are the answers.