Event 1: Mystery

Next year Xavier will be three times as old as his sister Yvonne, and two years after that he will be twice as old as Yvonne.
How old is Xavier?
Jackie has 12 coins, all quarters and nickels. After trying to empty her pockets by spending half her money on vending machine snacks, she still has 12 coins, all quarters and nickels.
What is the largest amount of money Jackie could have spent?
Given a set of points on a plane, an ordinary line is a line that passes through exactly two of the points but cannot be extended to pass through any of the others.
What is the largest number of points that can be arranged on a plane so that only three ordinary lines can be drawn?

1.    ____________ years
2. $ ____________ 
3.    ____________ points

Event 2: Geometry

Angles ABC and CBD are complementary. Angles CBD and DBE are supplementary.
What is the smallest possible measure of angle ABE?
In the diagram below, AB is parallel to DE. What is x? jump -50 fd 50 label 'A', above rt 90 pen black fd 100 label 'B', above label '145°', below rt 35 fd 100 label 'C', right label 'x°', left rt 114 fd 150 label 'D', left label '31°', -> @turnto 0; @jump 50, 10 lt 149 fd 100 label 'E', right ht()
How many degrees are between the minute hand and the hour hand of an analog clock when it is 2:40 PM?

1.   ____________ degrees
2.   ____________ degrees
3.   ____________ degrees

What is the largest prime number whose digits add up to a multiple of three?
The two digit number AB is prime, and the three digit number AB5 is a divisible by 9 and 7.
What is AB?
What is the sum of all the factors of 360?

1.   ____________
2.   ____________
3.   ____________

Consider the set of numbers {1, 1, 2, 3, 5, 8, 13, 21}.
If A is the mean, B is the median, and C is the mode of the set, then what is A - B - C?
Evalutate the following:

6⁵⁸ − 8 × 6⁵⁶

4²⁹ · 3^{14 · 4}
What single number could be added to the set in problem #1 that would make the the answer of (A - B - C) be equal to 2? (There are two answers. Try finding both.)

1.   ____________
2.   ____________
3.   ____________