2025 Team Up Challenge

Instructions for Teachers

This document provides instructions for running the Team Up Challenge. The instructions should be used as a suggestion only; teachers should feel free to make modifications in order to suit their classes. Ideally there should be four students per team, however this matters more for the relay than the other three parts.

Preparing Materials

In advance of running the Team Up Challenge, we recommend teachers prepare each part as indicated below. Students may want to use scrap paper and calculators as well.

Part	Instructions
Team Paper	Print one copy of the problems per student and one answer sheet per team.
Crossnumber Puzzle	Print one copy of the puzzle sheet and clue sheets per team.
Logic Puzzle	Print one clue sheet and one answer sheet per student.
Relay	Print one copy of the problems and one answer sheet per team. Cut the problem sheets on the dotted lines.

Team Paper

Approximately 30 - 40 minutes

The paper contains 15 problems of increasing difficulty. Team members are encouraged to collaborate when solving the problems and should decide on a strategy for sharing the work. It is unlikely that there will be enough time for everyone to do every question.
Final answers are to be written on the Team Paper Answer Sheet.

Crossnumber Puzzle

Approximately 20 - 30 minutes

The team should divide themselves into two pairs; one pair will take the across clues and the other pair will take the down clues. The team will write their answers on the shared Crossnumber Puzzle sheet as they work through the puzzle.
The crossnumber puzzle is designed so that some clues make it possible to find a number directly, some clues rely on an answer from another clue, and other clues require a partially completed puzzle board. Since each pair within a team is working on a different set of clues, the pairs will need to work together to completely solve the puzzle.
If teams are struggling to start the puzzle, teachers can direct them to across clues 12, 18, 24, and 25, or down clues 3, 11, 17, and 25.

Logic Puzzle

Approximately 20 - 30 minutes

Students use the clues to solve the puzzle. Note that the clues are not given in a specific order, and at times students will need to combine the information given in several different clues.
Students can work through the puzzle individually, in pairs, or as a team. Answer sheets are provided for all students so team members have the option to work individually and then compare their work in order to find a solution they all agree with.
Students are encouraged to use the answer sheet to write any information they know from the clues in order to help them reach the final answer.
If students are struggling to start the puzzle, teachers can direct them to clues 3 and 5.
Teams hand in only one Logic Puzzle Answer Sheet.

Relay

Approximately 5 - 10 minutes per relay

The "Practice Relay" is intended to be used as a practice round so students can understand the way the relay works. The questions in the Practice Relay are easier than the rest of the relay questions. Also, Player 1’s questions are the easiest in all relays.
Each team member is assigned a number: 1, 2, 3, or 4. Each number corresponds to a specific problem in each relay. Players 2, 3, and 4 require the answer from Players 1, 2, and 3, respectively, to solve their problem. This is indicated in the problem with the phrase "Replace $N$ below with the number you receive." However, Players 2, 3, and 4 should be able to do some work on their problem while they’re waiting for the answer from their teammate.
The four team members should not see any of the relay problems in advance and should not talk to each other during the relay.
Before the relay starts, each student should have their relay problem face down in front of them. Player 1 should have the answer sheet.
Once the relay starts, all players can flip over their paper and start working on their problem. Even Players 2, 3 and 4 should be able to do some work on their problem right away.
When Player 1, Player 2, or Player 3 thinks they have the correct answer to their problem, they record their answer on the answer sheet and pass the sheet to the next player. Students should write only the numeric part of their answer and not include any units. When Player 4 thinks they have the correct answer to their problem, they record their answer on the answer sheet and wait for their teacher to check it.
If all four answers are correct, the relay is complete! Otherwise, the teacher will mark the relay as incorrect and pass the answer sheet back to Player 1 so the team can try again. The answer sheet has space for two attempts for each relay.

Team Paper

Tips to Get Started

The questions in this paper increase in difficulty as you move through the paper. The last few questions require some careful thought.
Each team member doesn’t need to do every question. You can split the questions up, work together, or do a combination of both. Come up with a strategy that works for your team.

Questions

If the temperature in Whitehorse is −16℃ and the temperature in Kitchener is 3℃, how many degrees warmer is it in Kitchener than Whitehorse?
The coordinates of three of the vertices of a rectangle are $(1,2)$, $(7,2)$, and $(7,4)$, as shown. What are the coordinates of the fourth vertex of the rectangle?
Sofia draws $16$ identical small squares. Some of these squares are then shaded, as shown. How many more squares must be shaded so that $75\%$ of the squares are shaded?
Eight lily pads are arranged in a circle. A frog hops from one lily pad to the next in a clockwise direction. The frog begins on lily pad $3$, as shown.

After $75$ hops, which lily pad will the frog be on?
Each of the numbers $1$, $2$, $3$, $4$, and $5$ is placed in exactly one of the boxes so that each of the five fractions is equal to an integer. Then, the five fractions are added together, as shown in the sum below. \[\dfrac{12}{\Large\Box} + \dfrac{13}{\Large\Box} + \dfrac{14}{\Large\Box} + \dfrac{15}{\Large\Box} + \dfrac{16}{\Large\Box}\] What is the value of the sum?
Adian, Bagus, Chandra, Daisuke, and Ebba are sitting around a circular table.

Bagus sits in the chair between Adian and Daisuke. Ebba is not beside Daisuke. Which two people are sitting next to Ebba?
Ekain has eight strips of paper containing drawings, as shown.
Eight rectangular strips labelled A through H. Each strip has patterns drawn in vertical columns covering length of the strip. Five narrower strips have 2 patterns each and three wider strips have 3 patterns each. From left to right, the patterns on the strips are as follows:
1. jagged line, stars, dots
2. grid, stars
3. hearts, squiggly lines
4. jagged line, triangles
5. squiggly lines, triangles, swirls
6. grid, squares
7. swirls, triangles
8. stars, dots, squares
He takes some of these strips and arranges them side by side to create larger pictures. He can rotate the strips, but he cannot overlap them. Which strips did Ekain use to create the following picture?
The operation $\triangledown$ is defined as $a \triangledown b = 3a+b$. If $a \triangledown 5 = 26$, what is the value of $a$?
There are $35$ squares in a row. Ana draws a smiley face in the first square, and then in every third square after that. Sameer draws a flower in the second square, and then in every fourth square after that, as shown. How many squares will contain both a smiley face and a flower?
A palindrome is a positive integer that is the same when read forwards or backwards. For example, $545$ and $3773$ are both palindromes. Determine the largest five-digit palindrome whose digits have a sum of $15$.
In the diagram, the outer square has an area of $144 \text{ cm}^2$, the inner square has an area of $16 \text{ cm}^2$, and the four rectangles are identical. Determine the perimeter of one of the four identical rectangles.
Vanessa has $30$ red marbles, $30$ blue marbles, and $30$ green marbles. For each of the three colours, half of the marbles are sparkly. Vanessa places all of these marbles in a bag and randomly draws one. What is the probability that it is a sparkly green marble?
Triominoes are made of three squares and come in two shapes,
and .

By placing triominoes side by side, without overlapping them, it’s possible to make some of the following patterns. Note that it is possible to rotate the triominoes. Which of the patterns can be made?

$A$

$B$

$C$

$D$

$E$

$F$
Each pattern is made up of connected identical squares and can be viewed as a portion of a 5 by 5 grid of squares. The squares that are included in each pattern are as follows:
1. The third square in row 1, all five squares in row 2, the third square in row 3, and the second and third squares in row 4.
2. The first four squares in each of the first four rows, except for the first square in row 2.
3. All five squares in row 1, the middle three squares in row 2, and the middle square in each of row 4 and row 5.
4. The third and fourth squares in row 1, the third square in row 2, the first four squares in row 3, the last three squares in row 4, and the third and fifth squares in row 5.
5. The middle three squares in each of row 1 and row 2, and all five squares in row 3.
6. The first two squares and the last two squares in row 1, all five squares in row 2, the third and fourth squares in row 3, and the last four squares in row 5.
Seven points are arranged into two rows, with three points in the top row and four points in the bottom row, as shown.

Julie chooses three points, with at least one point from each row, and connects the points with straight lines to form a triangle. Three triangles that Julie could form are shown.

Determine the total number of triangles that Julie can form.
Chun and Rashid share a rectangular garden. The ratio of the area of Chun’s portion to the area of Rashid’s portion is $3:2$. They each plant daisies and tulips on their portion of the garden. On Chun’s portion of the garden, the ratio of the area covered by daisies to the area covered by tulips is $2:1$.

If half of the area of the entire garden is covered by daisies and half is covered by tulips, what is the ratio of the area covered by daisies to the area covered by tulips on Rashid’s portion?

Answer Sheet

Question	Answer
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Crossnumber Puzzle

Grid

Below is a $9$ by $9$ puzzle grid with each square either white or black. Each of the black squares is marked with the letter B. Twenty-eight of the white squares are marked with the numbers 1 through 28.

1	B	2	3	B	4		5	B
	B	B	6	7		B	8	9
10	11		B		B	B	12
B		B	13		14	B	B
15				B	16		17
	B	B	18	19		B		B
20	21	B	B		B	22		23
24		B	25		26	B	B
B	27			B	28		B

Tips to Get Started

This puzzle is like a crossword puzzle, except that the answers are numbers instead of words. Each empty square in the puzzle is to be filled with one digit.
Your team will work together, with some of you solving the across clues and some solving the down clues. Start by looking for clues that can be solved right away. Then move on to the clues that rely on an answer from another clue.

Clues

Across Clues

A number whose digits sum to $8$.
A multiple of $\boxed{\text{2 ACROSS}}$.
The area of a triangle with base $\boxed{\text{3 DOWN}}$ and height $\boxed{\text{25 DOWN}}$.
A number that is the product of two equal integers.
The mean of $\boxed{\text{1 DOWN}}$ and $\boxed{\text{18 ACROSS}}$.
The number of years in a decade.
A number whose tens digit is the mean of its other two digits.
A number that is the same when the digits are written in reverse order.
The product of three consecutive integers.
The sum of the numbers from $11$ to $19$, inclusive.
A factor of $\boxed{\text{17 DOWN}}$.
The smallest whole number that is divisible by both $8$ and $\boxed{\text{25 DOWN}}$.
The perimeter of a triangle with side lengths $13$, $21$, and $25$.
The positive difference between $987$ and $234$.
A number whose digits are three consecutive integers, in some order.
A prime number.

Down Clues

The area of a rectangle with length $\boxed{\text{24 ACROSS}}$ and width $\boxed{\text{3 DOWN}}$.
The largest number that both $120$ and $165$ are divisible by.
A multiple of $9$.
A number whose digits multiply to $36$.
A number whose digits are the same as the digits of $\boxed{\text{27 ACROSS}}$, but not necessarily in the same order.
A number that lies between $4025$ and $4035$ on the number line.
The number of apple fritters in a box containing $11$ dozen.
The mean of the three digits in this number is $5$.
This number appears in the sequence where the first term is $61$ and each term after the first is $\boxed{\text{24 ACROSS}}$ more than the previous term.
The result when $\boxed{\text{4 ACROSS}}$ is multiplied by $\boxed{\text{3 DOWN}}$ and then added to $25$.
The number that is $50\%$ of $462$.
The mode of the three digits of this number is $3$.
The sum of the digits of this number is equal to the sum of the digits of $\boxed{\text{15 ACROSS}}$.
The value of $7 + \boxed{\text{6 ACROSS}} - 1.5 \times 200$.
The number of quarters (worth $\$0.25$ each) needed to make $\$19.50$.
The positive difference between the two digits of this number is $6$.

Logic Puzzle

Puzzle

Ami’s Airport Taxi brought five passengers to the airport yesterday, each leaving on a different flight.

Using the clues below, determine the passenger name, destination, and purpose for travel for each of the departure times in the table on the next page.

The five people are Helenka, Iveta, the person visiting family, the person going to Tokyo, and the person leaving at 5:15 p.m.
Tuur left one hour after the person going to Rome, who was travelling for school.
Mijo left at 1:15 p.m. and was going on vacation. He was not the person going to Halifax.
Gaurav and Helenka were two of the passengers. Only one of them went to Vancouver.
Two people were traveling for business. They left five hours apart and went to Vancouver and Paris, in some order.

Tips to Get Started

You are encouraged to use the answer sheet to write any information you know from the clues in order to help you solve the puzzle.
Note that the clues are not given in a specific order, and at times you will need to combine the information given in several different clues.

Answer Sheet

Fill in the table with the passenger name, destination, and purpose for travel for each of the given departure times.

Departure Time	Passenger’s Name	Destination	Purpose
12:15 p.m.
1:15 p.m.
4:15 p.m.
5:15 p.m.
6:15 p.m.

Relay

Practice Relay

Player 1

The number of schools in each of three towns is shown in the bar graph. What is the total number of schools in the three towns?

The town Amere has 2 schools, the town Brix has 3 schools, and the town Creeke has 2 schools.

Player 2

Replace $N$ below with the number you receive.

Chef Carina puts $5$ slices of ham on each of her pizzas. How many slices of ham are needed to make $N$ pizzas?

You can start working on this question while you’re waiting for Player 1's answer.

Player 3

Replace $N$ below with the number you receive.

The three angles in a triangle are $25\degree$, $N\degree$, and $x\degree$. What is the value of $x$?

You can start working on this question while you’re waiting for Player 2's answer.

Player 4

Replace $N$ below with the number you receive.

Yusuf has $400$ flyers to deliver. He delivers $\frac{1}{2}$ of them on Monday and then delivers $N$ flyers on Tuesday. How many flyers are left to deliver after Tuesday?

You can start working on this question while you’re waiting for Player 3's answer.

Relay A

Player 1

Points $A$, $B$, and $C$ are on a number line. Point $B$ is halfway between $A$ and $C$. If $A$ is at $5$ and $B$ is at $9$, then where is $C$?

Player 2

Replace $N$ below with the number you receive.

If $x=10$, then what is the value of $\dfrac{7 \times x}{2}-N$?

You can start working on this question while you’re waiting for Player 1's answer.

Player 3

Replace $N$ below with the number you receive.

Evie has $60$ marbles. Prakash has $\frac{3}{4}$ as many marbles as Evie. Gloria has $N$ more marbles than Prakash. How many marbles do they have in total?

You can start working on this question while you’re waiting for Player 2's answer.

Player 4

Replace $N$ below with the number you receive.

A shape can be divided into a triangle, a square, and a rectangle, as shown.

A square with side length 9 is placed on the left side of a rectangle so that the bases of the two shapes line along the same horizontal line. The rectangle has vertical width 6 and the two bases together have length 20. A triangle is placed on top of the square so that its base aligns with the top side of the square.

If the total area of the shape is $N$, what is the area of the triangle?

You can start working on this question while you’re waiting for Player 3's answer.

Relay B

Player 1

What number should be subtracted from $2$ to give the result of $-6$?

Player 2

Replace $N$ below with the number you receive.

The first number in a sequence is a positive integer, and then each number after that is one more than the previous number in the sequence. If the $4$^th and $5$^th numbers add to $13$, what is the $N$^th number in the sequence?

You can start working on this question while you’re waiting for Player 1's answer.

Player 3

Replace $N$ below with the number you receive.

A number is multiplied by $N$ and then $14$ is added to that product, resulting in $134$. What is the original number?

You can start working on this question while you’re waiting for Player 2's answer.

Player 4

Replace $N$ below with the number you receive.

A box contains pears, apples, and oranges. There are $N$ pears, $9$ apples, and the number of oranges is one-third the number of apples. A fruit is randomly chosen from the box. What is the probability that the fruit is an apple?

You can start working on this question while you’re waiting for Player 3's answer.

Relay C

Player 1

Penny has $\$360$ in $\$20$ bills. How many $\$20$ bills does she have?

Player 2

Replace $N$ below with the number you receive.

A square is made up of four smaller squares, as shown.

A horizontal line and a vertical line divide a larger square into a 2 by 2 grid made up of four identical smaller squares.

If each of the smaller squares has a perimeter of $N$, what is the perimeter of the larger square?

You can start working on this question while you’re waiting for Player 1's answer.

Player 3

Replace $N$ below with the number you receive.

Determine the perimeter of the given shape.

You can start working on this question while you’re waiting for Player 2's answer.

Player 4

Replace $N$ below with the number you receive.

Sevil and Marjatta started work on the farm at the same time. Sevil spent $N$ minutes picking strawberries and then $55$ minutes planting lettuce. Marjatta spent $2$ hours and $15$ minutes cleaning the stables and then $93$ minutes feeding the animals. How many minutes before Marjatta did Sevil finish her work?

You can start working on this question while you’re waiting for Player 3's answer.

Answer Sheet

**Practice Relay**
	Player 1	Player 2	Player 3	Player 4	Teacher
1^st Attempt
2^nd Attempt

**Relay A**
	Player 1	Player 2	Player 3	Player 4	Teacher
1^st Attempt
2^nd Attempt

**Relay B**
	Player 1	Player 2	Player 3	Player 4	Teacher
1^st Attempt
2^nd Attempt

**Relay C**
	Player 1	Player 2	Player 3	Player 4	Teacher
1^st Attempt
2^nd Attempt

1	B	2	3	B	4		5	B
	B	B	6	7		B	8	9
10	11		B		B	B	12
B		B	13		14	B	B
15				B	16		17
	B	B	18	19		B		B
20	21	B	B		B	22		23
24		B	25		26	B	B
B	27			B	28		B

1	B	2	3	B	4		5	B
	B	B	6	7		B	8	9
10	11		B		B	B	12
B		B	13		14	B	B
15				B	16		17
	B	B	18	19		B		B
20	21	B	B		B	22		23
24		B	25		26	B	B
B	27			B	28		B

1	B	2	3	B	4		5	B
	B	B	6	7		B	8	9
10	11		B		B	B	12
B		B	13		14	B	B
15				B	16		17
	B	B	18	19		B		B
20	21	B	B		B	22		23
24		B	25		26	B	B
B	27			B	28		B