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2023 Beaver Computing Challenge
(Grade 5 & 6)

Questions

Part A

Beaver Hats

Five hats are hanging as shown.

Hat P is the second shortest hat. Hat Q is the tallest hat. Hat R is the shortest hat. Hat S is the third tallest hat. Hat T is the second tallest hat.

Question

In what order should the hats be rehung so that they get taller as you move left to right?

  1. \(R,P,S,T,Q\)
  2. \(Q,S,T,P,R\)
  3. \(R,P,T,S,Q\)
  4. \(T,Q,S,P,R\)

Flower Garden

Beaver Bai has a garden with 9 fence posts around the edge, as shown.

He uses yellow ropes to divide the garden into smaller sections, according to the following rules:

Question

Which of the following gardens below could Bai have made?

Karla’s House

Karla has three maps that all show exactly the same region. One map shows the forests , one shows the rivers , and one shows the houses . Karla's house is in the forest, touches the bank of the river, and is House A, B, C, or D.

Each of the three maps is divided into a 12 by 12 grid of squares. Houses A and D are located in squares covered by a forest, and houses B and C are not. Houses A and B are located in squares touching the bank of the river, and houses C and D are not.

Question

Which house is Karla’s house?

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

Umbrella

Story

This is a view of Andrew’s umbrella from above. The umbrella has 10 sections, each with a different design.

A top view of the umbrella showing then 10 sections around the centre. Moving counter clockwise around the sections, the designs in order are: small dots, large dots, waves, gridlines, thick stripes, thin stripes, circles, squares, triangles, solid black.

Question

Which of the following images shows a possible side view of Andrew’s umbrella?

  1. A side view of the umbrella showing five sections in a row. From left to right, the designs on the sections are: thick stripes, gridlines, waves, large dots, solid black.
  2. A side view of the umbrella showing five sections in a row. From left to right, the designs on the sections are: thin stripes, circles, squares, solid black, triangles.
  3. A side view of the umbrella showing five sections in a row. From left to right, the designs on the sections are: small dots, large dots, waves, gridlines, thick stripes.
  4. A side view of the umbrella showing five sections in a row. From left to right, the designs on the sections are: gridlines, waves, large dots, small dots, solid black.

Part B

Hamburger Shop

Story

Masahiro made a hamburger for a customer, but the customer changed their mind several times while giving their order.

Masahiro built the hamburger in the order shown from left to right, always putting new items on top. The X symbol means that the customer changed their mind about the most recently added item, so Masahiro removed the item on top.

bottom bun patty cheese patty X X tomato X patty tomato lettuce top bun

Question

Which of the following hamburgers did Masahiro make?

  1. From bottom to top, the items in the hamburger are bottom bun, patty, cheese, patty, tomato, lettuce, top bun.
  2. From bottom to top, the items in the hamburger are bottom bun, patty, patty, tomato, lettuce, top bun.
  3. From bottom to top, the items in the hamburger are bottom bun, patty, tomato, tomato, lettuce, top bun.
  4. From bottom to top, the items in the hamburger are bottom bun, patty, cheese, patty, patty, tomato, lettuce, top bun.

Tile Land

Story

Tiles that show blue areas of water and green areas of land are placed together to create landscapes. Tiles must be placed so that when tiles share an edge, land always touches land and water always touches water. For example, two tiles may be placed as shown on the left, but not as shown on the right:

   

Question

If the following two tiles have been placed as shown, which tiles can be placed in the grey areas?





Riccas

Story

Evren is trying to learn what a Ricca looks like. Evren studies photos of the following five Riccas and makes some notes that accurately describe what she sees.

Evren is then shown this sixth photo of a Ricca and realizes one of her notes is definitely wrong:

The sixth Ricca has two eyes, six teeth, two arms, five legs, two horns but no wings.

Question

Which one of Evren’s notes about Riccas is definitely wrong?

  1. Riccas always have teeth.
  2. Riccas sometimes have wings.
  3. Riccas have either horns or three eyes, but not both.
  4. Riccas have the same number of arms as legs.

Levers

Story

Jacinta’s new helicopter has a control panel with four levers that each control a different system.

The labels on the levers are missing, and Jacinta was told that the system was wired in a confusing way so she doesn’t know which lever controls which system. All she knows is that putting a lever up turns one system and its indicator light on, and putting a lever down turns one system and its indicator light off.

The image shows which indicator lights are on for three different configurations of the levers.

The first configuration has levers 1 and 3 down and levers 2 and 4 up. In this case, the indicator lights for the heating and ventilation systems are on and the other two lights are off. The second configuration has levers 1, 2, and 4 up, and lever 3 down. In this case, the indicator lights for the heating, ventilation, and humidity systems are on and the other light is off. The third configuration has levers 1, 3, and 4 up, and lever 2 down. In this case, the indicator lights for the ventilation, lights, and humidity systems are on and the other light is off.

Question

Which of the following correctly matches each lever to the system that it controls?

  1. 1: heat. 2: ventilation. 3: lights. 4: humidity.
  2. 1: humidity. 2: ventilation. 3: lights. 4: heat.
  3. 1: humidity. 2: heat. 3: lights. 4: ventilation.
  4. 1: ventilation. 2: heat. 3: lights. 4: humidity.

Part C

Snail Compress

Story

A beaver has a special technique to shrink images.

First, they cut the original image into 10 equally-sized vertical strips. Then, they remove the even-numbered strips and assemble the odd-numbered strips to create a new image.

Next, they cut the new image into 10 equally-sized horizontal strips. Then, they remove the even-numbered strips and assemble the odd-numbered strips to create a complete shrunken image. Here is an example:

An alternative format for the example follows.

Question

If the beaver uses this technique to shrink the image below, what is the complete shrunken image?

An alternative format for the diagram follows.

  1. Option A is a five by five grid with cells coloured green, yellow, black, or white. An alternative format for Option A follows.

  2. Option B is a five by five grid with cells coloured green, yellow, black, or white. An alternative format for Option B follows.

  3. Option C is a five by five grid with cells coloured green, yellow, black, or white. An alternative format for Option C follows.

  4. Option D is a five by five grid with cells coloured green, yellow, black, or white. An alternative format for Option D follows.

Unloading

Story

Freight trains consist of an engine followed by wagons, each holding a numbered box. The boxes must be unloaded in increasing order, starting from box 1. To unload a box, its wagon must be positioned directly below the crane.

The crane is in a fixed position and trains can only move forward on a loop. Usually, this means that several rounds are needed to unload all the boxes. Each round begins with the engine directly under the crane.

An engine followed by four wagons is on a track forming a loop. Each wagon has a box labelled with a different number. From front to back, the numbers are 4, 1, 3, and 2. The engine is under a crane placed over the track.

In the example shown, the boxes have to be unloaded in the order 1, 2, 3, 4 and three rounds are needed to do this. In the first round of unloading, the train moves forward to skip box 4, unload box 1, skip box 3, and unload box 2. The train then goes around the track until the engine is under the crane again. In the second round of unloading, the train moves forward to skip box 4, skip the empty wagon, and unload box 3. The train then has to come back for a third round in order to unload box 4.

Question

How many rounds will be needed to unload all the boxes from the following train?

An engine followed by ten wagons. Each wagon has a box labelled with a number from 1 to 10. From front to back, the numbers are 10, 3, 9, 7, 1, 6, 2, 8, 5, and 4.

  1. 5
  2. 6
  3. 7
  4. 8

Decorated Mat

Story

Ángel has the decorated mat shown below on the left and the pattern shown below on the right.

A mat made of 9 squares arranged into a 3 by 3 grid. In the top row, the squares all have a green star. In the middle row, the first and last squares have an orange circle and the middle square has a blue diamond. In the bottom row, the first square has an orange circle, the middle square has a green star, and the last square has a blue diamond.   Three squares placed in a capital L shape. The corner square has a blue diamond. The square above the corner square has an orange circle. The square to the right of the corner square has a green star.

They determine that the pattern appears twice on the mat. Note that they may rotate the pattern but they may not turn it over.

On the mat, the middle square in the top row (with a green star), and the first two squares in the middle row (with an orange circle then a blue diamond) are highlighted. These squares form the L shaped pattern rotated 90 degrees counter clockwise.   On the mat, the last two square in the middle row (with a blue diamond then an orange circle) and the middle square in the bottom row are highlighted. These squares form the L shaped pattern rotated 90 degrees clockwise.   On the mat, the first two square in the middle row (with an orange circle then a blue diamond) and the middle square in the bottom row are highlighted. These squares form the L shaped pattern but flipped over. A large X crosses out this highlighted L shape.

Then Ángel looks at the new mat shown below on the left for the new pattern shown below on the right.

   A description of the mat and pattern follow.

Question

How many times does this new pattern appear on the new mat if Ángel may rotate the pattern but not turn it over?

  1. 3
  2. 4
  3. 7
  4. 9

Sprinklers

Story

Plots of land on Qi’s farm are arranged in an 8-by-8 grid. The 64 plots contain four types of plants as shown.

An alternative format for the farm diagram.

Ali wants to install sprinklers so that each plot is watered by exactly one sprinkler. All the plots watered by a single sprinkler must be the same type of plant. There are three types of sprinklers:

Question

What is the minimum number of sprinklers that Qi needs?

  1. 19
  2. 21
  3. 23
  4. 25