November 2025 Contest — Grade 6
The November 2025 North Star contest paper for Grade 6 has 12 questions and a 60-minute limit. Two sample questions with worked solutions are below, and you can take the whole paper online for free — no account, no sign-up.
- Grade
- Grade 6
- Questions
- 12
- Time limit
- 60 minutes
- Contest
- November 2025
- Subject
- Mathematics
- School year
- 2025-26
Before you start
- The timer starts when you press Start and runs for 60 minutes.
- Answer the 12 questions in any order; each is multiple choice.
- Your answers are marked as you go. Nothing is saved to an account, so finish in one sitting.
Sample questions
The first and last questions from this paper, with their worked solutions.
Question 1 — Geometry & Measurement
Jane glued together 27 one cm cubes into a 3 cm by 3 cm by 3 cm cube. She then dips the large cube into a bucket of paint. How many cubes will have exactly 3 sides painted?
- A.8
- B.4
- C.6
- D.9
- E.12
Show the worked solution
To find the number of small 1 cm cubes that have exactly 3 sides painted, we need to look at where these cubes are located within the larger 3 cm by 3 cm by 3 cm cube.
When the large cube is dipped into paint, only the outer faces of the large cube get covered in paint.
Let's analyze the positions of the smaller cubes:
1. Corner cubes: These cubes are located at the corners of the large cube. Each corner cube has 3 of its faces exposed to the outside. Therefore, these cubes will have exactly 3 sides painted.
2. Edge cubes (excluding corners): These cubes are along the edges but not at the corners. Each of these has 2 faces exposed, so they will have exactly 2 sides painted.
3. Face-center cubes: These cubes are in the middle of each of the 6 faces of the large cube. Each has only 1 face exposed, so they will have exactly 1 side painted.
4. Center cube: This is the single cube in the very center of the 3x3x3 structure. It has no faces exposed, so it will have 0 sides painted.
Since a cube has exactly 8 corners, there are 8 small cubes located at the corners. Thus, exactly 8 cubes will have 3 sides painted.
The answer is A
Question 12 — Logical Reasoning & Problem Solving
Which of the following families (A, B, C, D, E) could have the most children? A family where
A. Each of 7 brothers have 2 sisters
B. Each brother has 4 sisters and each sister has 3 brothers
C. There are seven children
D. The number of sisters multiplied by number of brothers is less than 12
E. There are three more sisters than brothers and each sister has five brothers
- A.A
- B.B
- C.C
- D.D
- E.E
Show the worked solution
To find which family could have the most children, let's calculate the number of children in each scenario:
Family A: "Each of 7 brothers have 2 sisters."
Since all brothers belong to the same family, they share the same sisters. Thus, there are 7 brothers and 2 sisters.
Total children = 7 + 2 = 9 children
Family B: "Each brother has 4 sisters and each sister has 3 brothers."
Since each brother has 4 sisters, there are exactly 4 sisters in the family. Since each sister has 3 brothers, there are exactly 3 brothers in the family.
Total children = 3 + 4 = 7 children
Family C: "There are seven children."
Total children = 7 children
Family D: "The number of sisters multiplied by number of brothers is less than 12."
Let's find the maximum possible sum of brothers and sisters where their product is less than 12:
If there is at least 1 sister and 1 brother, the maximum sum occurs with 1 sister and 11 brothers (or vice versa), because 1 x 11 = 11 < 12. This gives 1 + 11 = 12 children.
If "sisters" and "brothers" must be plural (at least 2 of each), the maximum sum occurs with 2 sisters and 5 brothers (or vice versa), because 2 x 5 = 10 < 12. This gives 2 + 5 = 7 children.
In either case, the maximum number of children is at most 12.
Family E: "There are three more sisters than brothers and each sister has five brothers."
Since each sister has 5 brothers, there are exactly 5 brothers in the family. Since there are 3 more sisters than brothers, the number of sisters is 5 + 3 = 8 sisters.
Total children = 5 + 8 = 13 children
Comparing the totals, Family E has the most children with 13.
The answer is E
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.