Standard One – Foundation Level Problems
Prompt: How many pairs of integers can be picked from the set {1,2,3,…41} with the
property that the sum of the integers is even?
Answer: 400
Mathematics Teacher December 1995 V88 N9
Prompt: What is the first two-digit prime number for which the product of its digits is
equal to the sum of its digits plus 7?
Answer: 29
Mathematics Teacher December 1995 V88 N9
Prompt: A number of robbers were discussing how best to share some stolen rolls of
cloth. They said that if each robber had six rolls, five rolls would be left, but if each had
seven rolls, they would be eight rolls short. How many robbers had how many rolls of
cloth?
Answer: Thirteen robbers and eighty-three rolls
Mathematics Teacher December 1995 V88 N9
See Joseph Needham, Science and Civilisation in China, vol. 3 (New York: Cambridge University Press, 1959)
Prompt: A textbook is opened at random. What are the page numbers if the product of
the two facing pages is 2256?
The University of Northern Colorado, Math Contest, November 1994
Prompt: What is the sum of the first fifty positive integers?
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99.
Prompt: Sally is having a party. The first time the doorbell rings, one guest enters. If
on each successive ring a group enters that has 2 more guests than the group that
entered on the previous ring, how many total guests will have arrived after the 20 th ring?
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99.