St. Mary’s High School entered a basketball tournament. In the first round, each team played one game, and the losers dropped out. Each winner from the first round played one game in the second round, and the losers dropped out. This process continued until a winner was declared. St. Mary’s won the tournament by winning five games. How many teams were in the tournament?
Find the last three digits of the sum \displaystyle 625^{13} +376^{87} .
The average age of the students m" a group was 15. The average age of the teachers in the same group was 45. The average age of the whole group was 19. What was the smallest possible number of people m' the group?
The difference between the squares of two consecutive whole numbers is 63. What are the numbers?
A rectangular solid is to be made using 60 blocks, each of which is a 1-cm cube. Write a full solution to the following, showing your mathematical model and your reasoning.
a) How many rectangular solids are possible?
b) How many different surface areas are possible?
Suppose the land area of each province were divided equally among all the people living in that province. In which province would a person receive
a) the most land?
b) the least land?
Dylan is meeting his sister and four of her friends for lunch. The five women are named Alicia, Rachel, Lani, Donna, and Casey. Three of the women are under 30 years old, and two are over 30. Two of the women are lawyers, and three are doctors. Alicia and Lani are in the same age group. Donna and Casey are in different age groups. Rachel and Casey have the same profession. Lani and Donna have different professions. Dylan’s sister is a lawyer and is over 30. Who is Dylan’s sister?
There are three piles of toothpicks, one with 11 toothpicks, one with 7, and the third with 6. You are to get 8 toothpicks in each pile in three moves. In each move, you must add to any pile exactly as many toothpicks as it already has, and all the toothpicks moved must come from a single pile.
What percent of Canadians live in coastal communities?