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Stage 1 · Combinatorics

10 problems · · mathsolympiadprep.com

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1. In the diagram, how many of the shapes are triangles?

   1. A$4$
   2. B$5$
   3. C$6$
   4. D$7$
   5. E$8$

   Combinatorics Solution and answer checking →

2. In the diagram, how many of the $24$ circles are shaded?

   1. A$10$
   2. B$12$
   3. C$14$
   4. D$16$
   5. E$18$

   Combinatorics Solution and answer checking →

3. How many ☐ symbols are in the figure?

   $24$
   $20$
   $15$
   $17$
   $25$

   Combinatorics Solution and answer checking →

4. The graph shows the number of text messages received by Tanner in a given week.

   
   Hide/Reveal Description of Texts

   Monday, 30
   Tuesday, 28
   Wednesday, 20
   Thursday, 10
   Friday, 50
   Saturday, 45
   Sunday, 40

   On what day did Tanner receive the most text messages?

   1. A$\textrm{Friday}$
   2. B$\textrm{Tuesday}$
   3. C$\textrm{Thursday}$
   4. D$\textrm{Saturday}$
   5. E$\textrm{Wednesday}$

   Combinatorics Solution and answer checking →

5. Based on the graph shown, which sport is played by the most students?

   
   Hide/Reveal Description of Students Playing Sports

   Hockey, 40
   Basketball, 30
   Soccer, 50
   Volleyball, 20
   Badminton, 10

   1. A$\text{hockey}$
   2. B$\text{basketball}$
   3. C$\text{soccer}$
   4. D$\text{volleyball}$
   5. E$\text{badminton}$

   Combinatorics Solution and answer checking →

6. In the diagram, the pie chart shows the results of a survey asking students to choose their favourite fruit.

   Combinatorics Solution and answer checking →

7. The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots.
   Three of the faces are shown.

   What is the total number of dots on the other three faces?

   1. A$6$
   2. B$8$
   3. C$10$
   4. D$12$
   5. E$15$

   Combinatorics Solution and answer checking →

8. A six-sided die has the numbers one to six on its sides. What is the probability of rolling a five?

   1. A$\frac{2}{6}$
   2. B$\frac{1}{6}$
   3. C$\frac{5}{6}$
   4. D$\frac{3}{6}$
   5. E$\frac{4}{6}$

   Combinatorics Solution and answer checking →

9. The graph shows the number of apples that each of five students
   ate during a week.

   Which student ate the greatest number of apples?

   1. ADae
   2. BJoe
   3. CEtta
   4. DSusie
   5. EVinh

   Combinatorics Solution and answer checking →

10. A pentagon is divided into 5 equal sections, as shown.

    An arrow is attached to the centre of the pentagon. The arrow is spun once. What is the probability that the arrow stops in the section numbered 4?

    1. A$\frac{3}{5}$
    2. B$\frac{1}{2}$
    3. C$\frac{4}{5}$
    4. D$\frac{1}{4}$
    5. E$\frac{1}{5}$

    Combinatorics Solution and answer checking →

Answer key — Stage 1 · Combinatorics

Worked solutions for every problem are on the site, one page per problem.

1. $C$ open
2. $B$ open
3. $E$ open
4. $A$ open
5. $C$ open
6. $D$ open
7. $B$ open
8. $D$ open
9. $A$ open
10. $C$ open

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