Standard Three – Top Level Problems
Prompt: At every meal, I drink cola, grapefruit juice, or mil; Marie-Claire drinks milk,
cola, or orange juice; and Dana drinks coffee, root beer, grapefruit juice, or orange juice.
We each have only one drink per meal, and none of us has any actual preference
among our potential beverages, so we select them randomly. What is the likelihood that
we all drink different drinks at lunch today?
Answer: 11/18
Mathematics Teacher April 1992 V85 N4
Prompt: Fifty tickets numbered consecutively from 1 to 50 are placed in a jar. Two are
drawn at random (without replacement). What is the probability that the difference of
the two numbers is 10 or less?
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99.
Prompt: There are 6 = 3! Permutations of 1,2,3. Treat each of these permutations as a
3-digit number. Compute the sum of these 6 numbers. Repeat with 1,2,3,4. (i.e.
Determine the sum of all permutations of 1,2,3,4.)
University of Northern Colorado Mathematics Contest
Prompt: There is just one integer value of n for which the median and the arithmetic
mean of the five numbers 15, 13, 17, 27, and n are equal. Find n.
University of Northern Colorado Mathematics Contest
Prompt: The ten guests at a party put their names on slips of paper and drop them in a
hat for a drawing. You decide to increase your chances of winning by writing your name
on two slips of paper. Just before the drawing, you learn that a second name will be
drawn for a second prize after the first name is drawn. What is the probability that your
name will be drawn twice, thus revealing your misconduct?
Mathematics Teacher, April 1998, V98 N4