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2025 Beaver Computing Challenge
(Grade 5 & 6)

Questions

Part A

Merging Cars

Story

Cars waiting to enter Main Street are shown. The cars take turns coming from Spruce Street and Oak Street.

From first to last, the five cars lined up on Spruce Street are green, orange, light blue, purple, and then red, and the six cars lined up on Oak Street are grey, white, dark blue, brown, yellow, and pink.

Question

If the first car comes from Spruce Street, which car will enter Main Street immediately after the purple car that is fourth in line on Spruce Street. ?

  1. Red car that is fifth in line on Spruce Street.
  2. Light blue car that is third in line on Spruce Street.
  3. Dark blue car that is third in line on Oak Street.
  4. Brown car that is fourth in line on Oak Street.

Building Instructions

Story

You have the following blocks:

Six cubes

One bridge

Two rectangular prisms

Your friend gives you the following building instructions:

  1. Take three cubes and place them on top of each other to form a tower.
  2. Form a separate tower with the three remaining cubes.
  3. Place the two rectangular prisms next to the cube towers.
  4. Place the bridge on top of some of the blocks.

These instructions allow you to build many different structures. Here are two examples:

Two towers of three cubes beside two upright rectangular prisms. The bridge is placed on top, but upside down, resting on the two towers and the two upright prisms.

Two towers of three cubes beside one upright rectangular prism and one rectangular prism on its side. The bridge is placed on top, but upside down, resting on the two towers and upright prism.

Question

Which of the following structures cannot be built by following the instructions?

  1. Two towers of three cubes beside two upright rectangular prisms. The bridge is placed on top resting on the two rectangular prisms.
  2. The bridge beside one upright rectangular prism. Two towers of three cubes and one upright rectangular prism are on top of the bridge.
  3. Two towers of three cubes beside two upright rectangular prisms. The bridge is placed on top resting on the two upright prisms.
  4. Two towers of three cubes beside one upright rectangular prism and one rectangular prism on its side. The bridge is placed on top resting on the two towers.

A Wrong Step

Story

Aira is walking from her house House A to her friend Bo's house House B for the first time. A map of the streets between their houses is shown. All streets go either east/west or north/south.

A map showing the different streets near House A and House B.

Bo gave Aira the following instructions, where walking one block means walking straight until you reach the next street.

  1. Step 1: Walk two blocks east (E).
  2. Step 2: Walk three blocks south (S).
  3. Step 3: Walk three blocks east (E).
  4. Step 4: Walk one block north (N).

However, Aira made a mistake with one of the steps and did not arrive at Bo's house. Her route is shown.

A path on the map from House A that does not end at House B.

Question

Which step did Aira not follow correctly?

  1. Step 1
  2. Step 2
  3. Step 3
  4. Step 4

Alex's Treasure

Story

Alex the explorer has found a treasure map. The map has a grid with different symbols, as shown.

A description of the map follows.

Alex must reach the treasure from the starting point, while following these three rules:

  1. They cannot step on water.

  2. They must cross at least one mountain.

  3. They can only move one square at a time. They can move up (\(\uparrow\)), down (\(\downarrow\)), left (\(\leftarrow\)), and right (\(\rightarrow\)). They cannot move diagonally.

Question

Four paths are shown below. Which path leads Alex to the treasure while following all the rules?

  1. The path moves up 4 squares then right 4 squares. It passes through 7 squares: 4 with grass, 2 with a mountain, and 1 with water.
  2. The path moves up 1, right 2, up 1, right 1, up 1, left 2, up 1, then right 3. It passes through 11 squares: 7 with grass and 4 with a mountain.
  3. The path moves 4 squares to the right, then diagonally up and left across a 3 by 3 grid, then up 1, then right 2. It passes through 9 square: 8 with grass and 1 with a mountain.
  4. The path moves right 4 squares then up 4 squares. It passes through 7 squares, all with grass.

Part B

Cube

Story

A Bebras cube has a different shape on each face. The six shapes on a Bebras cube are shown.

Circle Diamond Ellipse Pentagon Star Triangle

Eight identical Bebras cubes are stacked together to form a larger \(2 \times 2 \times 2\) cube, as shown.

A description of the cube follows.

Question

On a Bebras cube, what shape is on the face opposite the Circle ?

  1. Star
  2. Triangle
  3. Diamond
  4. Ellipse

Elevator

Story

Biwako and Kai live on different floors of the same apartment building.

They each have several boxes being delivered. Biwako's boxes are labeled B, and Kai's boxes are labeled K. However the boxes were mixed up and stacked in the elevator as shown.

A vertical tower of 8 boxes. From top to bottom, the boxes are labelled K, B, B, K, B, K, K, B.

Biwako and Kai each stay on their own floor. When the elevator arrives on their floor, they take all of their boxes that are on the top of the stack. Then the elevator moves directly to the other person's floor. The elevator continues to move back and forth between Biwako and Kai's floors until all the boxes have been taken.

The elevator first stops on Kai's floor.

Question

In total, how many times does the elevator stop before all the boxes have been taken?

  1. 2
  2. 3
  3. 5
  4. 6

Story

Beaver Arnie makes decorative banners using different shapes cut out of fabric. However he is very particular about the order of the shapes in the banner. In the following table, a ✓ between two shapes means they can be placed next to each other in a banner, and an ✗ means they cannot be placed next to each other in a banner.

Circle
 Square
 Heart
 Triangle
 Star
Circle
 ✗ ✗ ✓ ✗ ✓
Square
 ✗ ✗ ✓ ✓ ✗
Heart
 ✓ ✓ ✗ ✗ ✗
Triangle
 ✗ ✓ ✗ ✗ ✓
Star
 ✓ ✗ ✗ ✓ ✗

Question

Which of the following banners follows Beaver Arnie's rules?

  1. From left to right: triangle, square, star, heart, circle.
  2. From left to right: heart, square, triangle, circle, star.
  3. From left to right: circle, heart, square, triangle, star.
  4. From left to right: Square, heart, triangle, star, circle.

Spatial Reasoning

Story

Ximena is exploring a photo editing app on her phone. She transforms photos using the operations M and R, which are explained below.

Operation Description Example
M Mirror reflection from left to right
R Rotation 90 degrees clockwise

Ximena can also do multiple operations in a row. For example,

A rotation by 90 degrees clockwise, labelled R, followed by a mirror reflection, labelled M.

Now, Ximena starts with this photo: A beaver in a chair that forms a shape like a capital L. The back of the chair is vertical along the left edge of the picture. The seat of the chair is horizontal along the bottom edge of the picture..

She then performs all of the following operations in order from left to right: R R R R M R M.

Question

How will the photo look when Ximena is done performing all the operations?

  1. The back of the chair is horizontal along the bottom edge the picture. The seat of the chair is vertical along the right edge of the picture.
  2. The back of the chair is horizontal along the top edge of the picture. The seat of the chair is vertical along the left edge of the picture.
  3. The back of the chair is horizontal along the bottom edge the picture. The seat of the chair is vertical along the left edge of the picture.
  4. The back of the chair is vertical along the left edge of the picture. The seat of the chair is horizontal along the bottom edge of the picture.

Part C

Beaver Race

Story

Five beavers ran a race. Each beaver wore a hat with a different symbol on it. One minute into the race, the beaver wearing a purple hat was in last place. The order of the five beavers at that time is shown below.

Five beavers in a line each wearing a different coloured hat. From front to back in the line, the hat colours are red, blue, green, yellow, and purple.

After that, exactly three changes in position occurred:

Question

Which hat was the beaver who finished the race last wearing?

  1. blue hat
  2. green hat
  3. yellow hat
  4. purple hat

Visiting Grandparents

Story

Adriana wants to travel to her grandparents house by bus. In the map shown, there are seven cities and the cost of a bus ticket between two cities is written on the road connecting them. Adriana lives in the city labelled \(\text{A}\), while her grandparents live in the city labelled \(\text{G}\).

A description of the map follows.

Question

What is the least expensive total price for bus tickets from Adriana's city to her grandparents' city?

  1. 33
  2. 39
  3. 29
  4. 36

Exciting Water Slide

Story

A dynamic waterslide has three gates. When a beaver reaches a gate, the beaver is sent either left or right. This causes the gate to flip, sending the next beaver the other direction, as shown.

Little beaver Dan wants to try the waterslide. Mama beaver wants to know which slide Dan will come out of so that she can take a good picture. There were three beavers ahead of Dan. The first beaver came out of slide B and the second beaver came out of slide C, as shown.

There is one gate at the top of the slide. From this top gate, there is a left slide to a gate below on the left and a right slide to a gate below on the right. From the left gate, there is a left exit slide marked A and a right exit slide marked B. Down from the right gate, there is a left exit slide marked C and a right exit slide marked D.

Question

Which slide will Dan come out of?

  1. Slide A
  2. Slide B
  3. Slide C
  4. Slide D

Research Expeditions

Story

A research team needs to investigate some islands. The map shows all seven islands they need to investigate as well as the ferry routes between islands. Arrows indicate the directions of the ferries.

A description of the map follows.

During a research trip, the team lands by helicopter on an island of their choice, takes ferries to other islands, and returns to the original island where the helicopter is located. To visit every island at least once, it will take the team more than 1 research trip.

Question

What is the minimum number of research trips needed to visit every island at least once?

  1. 2
  2. 3
  3. 4
  4. 5