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2023 Beaver Computing Challenge
(Grade 9 & 10)

Questions

Part A

Photo

Story

A beaver took a photo looking directly down the centre of an arrangement of four logs assembled as shown.

Four logs are placed with their bases in a circle and their tops leaned in to meet at a point. There is a green log, then moving clockwise around the circle, there is an orange log, then a white log, then a brown log, and then back to the original green log.

Question

Which of the following could be the beaver’s photo?


  1. A top view of the logs. The log at the top of the photo is orange, then moving clockwise around the circle, there is a brown log, then a green log, then a white log, then back to the top orange log.

  2. A top view of the logs. The log at the top of the photo is green, then moving clockwise around the circle, there is an orange log, then a brown log, then a white log, then back to the top green log.

  3. A top view of the logs. The log at the top of the photo is orange, then moving clockwise around the circle, there is a green log, then a white log, then a brown log, then back to the top orange log.

  4. A top view of the logs. The log at the top of the photo is green, then moving clockwise around the circle, there is an orange log, then a white log, then a brown log, then back to the top green log.

Cards

Story

A card game has four types of cards:

A card with stripes, a card with a star, a card with a diamond, and a card with a semicircle.

The symbol on each card indicates the number of points the card is worth, as shown.

Symbol stripes star diamond semicircle
Number of Points \(8\) \(4\) \(2\) \(1\)

A player’s score is the total number of points of the cards they have in their hand.

For example, Zita has the cards star and diamond and her score is \(4+2=6\).

Question

If Silat’s score is \(9\), what cards could he have in his hand?

  1. Two cards: one with stripes and one with a diamond.
  2. Two cards: one with stripes and one with a semicircle.
  3. Three cards: one with stripes, one with a diamond, and one with a semicircle.
  4. Three cards: one with stripes, one with a star, and one with a semicircle.

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 shows the region divided into a 12 by 12 grid of squares. Houses A and D are located in squares covered by forests, 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

Video Game

Story

Sasha uses the numbers from 0 to 7 to move her character different directions in a video game, as shown.

A 3 by 3 grid with a beaver in the centre square and arrows labelled 0 through 7 pointing from the beaver to the eight outer squares showing eight different directions as follows: 0 is right, 1 is diagonally up and right, 2 is up, 3 is diagonally up and left, 4 is left, 5 is diagonally down and left, 6 is down, and 7 is diagonally down and right.

For example, to move her character clockwise along the grey path below and back to its original position, she types the sequence 1, 0, 7, 6, 4, 5, 3, 2.

In a 4 by 4 grid, the beaver starts in the first square in the second row and moves around the grid as follows: up and right (arrow 1), right (arrow 0), down and right (arrow 7), down (arrow 6), left (arrow 4), down and left (arrow 5), up and left (arrow 3), up (arrow 2).

Question

Which of the following sequences will move Sasha’s character clockwise along the grey path and back to its original position?

In a grid with 5 rows and 6 columns, the beaver starts in the square in row 3 and column 1. The following squares are grey: row 3 column 1, row 2 column 2, row 1 column 3, row 1 column 4, row 2 column 5, row 3 column 6, row 4 column 5, row 5 column 4, row 5 column 3, row 4 column 2.

  1. 1, 1, 7, 7, 5, 5, 3, 3
  2. 1, 1, 4, 7, 7, 5, 5, 0, 3, 3
  3. 1, 1, 0, 7, 7, 5, 5, 4, 3, 3
  4. 7, 7, 0, 1, 1, 5, 5, 4, 3, 3

Push the Button

Story

Numbered balls are stored in the device shown below. Pushing one of the buttons P, Q or R causes its gate to open and the first ball behind that gate to drop.

Three different paths blocked by gates lead to the same hole. The gate on the first path has button P. Behind this gate are four numbered balls: first is ball 4, followed by balls 8, 7, then 1. The gate on the second path has button Q and balls 3, 9, 4, then 11 behind it. The gate on the third path has button R and balls 2, 5, 6, then 10 behind it.

Question

What is the maximum number of button pushes that result in balls being dropped in increasing (but not necessarily consecutive) order?

  1. 6
  2. 7
  3. 8
  4. 9

Part B

Eating Carrots

Story

Four carrots are growing in four soil patches as shown.

Four patches of soil in a row from left to right. Each patch shows the top of one carrot.

Rabbits are capable of the following three actions:

  1. Arrow to the left Hop to the soil patch immediately to the left of the current soil patch.

  2. Arrow to the right Hop to the soil patch immediately to the right of the current soil patch.

  3. Carrot Eat the carrot growing in the current soil patch.

Earl the rabbit started in one of the four soil patches, but we do not know which one. We do know that Earl never jumped left of the leftmost soil patch nor right of the rightmost soil patch.

In addition, we know that Earl’s sequence of actions was:

arrow to the right carrot arrow to the left carrot arrow to the left arrow to the left carrot

Question

Which image below shows the soil patches and the one uneaten carrot after Earl finished his sequence of actions?

  1. The uneaten carrot is in the third soil patch from the left.
  2. The uneaten carrot is in the rightmost soil patch.
  3. The uneaten carrot is in the leftmost soil patch.
  4. The uneaten carrot is in the second soil patch from the left.

Bebras Ball

Story

Players are ranked from 1st place to 16th place based on their performance in a Bebras Ball tournament. The tournament consists of four rounds. All the players are grouped together for the first round, and divided into smaller groups after each round as shown. Winning players follow the left arrow to their group in the next round (or final rank). Losing players follow the right arrow to their group in the next round (or final rank).

A description of the diagram follows.

For example, a player who wins during rounds 1 and 2, but loses during rounds 3 and 4, will receive a rank of 4th place.

Question

If Noro played in the tournament and lost during exactly one round, which of the following ranks could he not receive?

  1. 2nd
  2. 3rd
  3. 5th
  4. 7th

Lockers

Story

When packages arrive at the post office they are placed in lockers to await pick up. The top row of lockers can only hold small packages. The middle row of lockers can hold small or medium packages. The bottom row of lockers can hold packages of any size. Each locker can only hold one package at a time.

The following image shows what the lockers at the post office currently look like. Lockers marked with an X are holding a package.

A description of the diagram follows.

When a new package arrives, it is placed in the lowest-numbered available locker in which it can fit. When a customer arrives to pick up a package from a locker, the locker becomes available again.

The post office has opened for the day and the following five events occur in this order:

Question

Then one more small package arrives. In which locker is it placed?

  1. 20
  2. 19
  3. 24
  4. 17

Island Vacation

Story

Ravi is on vacation in the Island Kingdom. On the map, each island is marked with a different shape, and the routes between islands are marked with the type of boat used on the route. There are two types of boats: sailboat and speedboat.

A description of the diagram follows.

Ravi started at the island marked with an X and traveled to the island marked with a star, possibly visiting some islands more than once.

Question

Which of the following sequences of boats could Ravi not have taken?

  1. speedboat speedboat sailboat speedboat
  2. sailboat speedboat sailboat speedboat sailboat speedboat
  3. sailboat sailboat speedboat sailboat speedboat
  4. speedboat speedboat sailboat sailboat speedboat

Moving Documents

Story

Every day, employees of Beaver Logistics must move documents in boxes from one site to another. It takes 1 minute per box to load the truck, 1 minute per box to unload the truck, and it is a 50 minute round trip between the two sites. The truck can hold at most 20 boxes and so moving more than 20 boxes requires more than one trip back and forth.

At the start of each day, there are 36 boxes of documents to be moved. However, it is possible to spend some time reorganizing to reduce the total number of boxes that then need to be moved.

Question

Who was able to move all the documents (including any time spent reorganizing), and return to the starting site in less than 3 hours?

  1. Alia and Yoko
  2. Alia and Bala
  3. Bala and Yoko
  4. Alia, Bala and Yoko

Part C

Magical Doors

Story

There are eight buildings, labelled A through H, along a road as shown below.

Each building has two doors and certain doors match. For example, there are three matching blue doors on buildings A, D, and E, and two matching green doors on buildings A and H. A complete description of the buildings can be found at the end of the Story.

The only way to travel between the buildings is by using magical doors. There are seven different types of doors:

Blue doors, purple doors, green doors, red doors, brown doors, orange doors, and black doors.

Each building has two different doors. When you exit a building through one of its doors, you can then enter any of the other buildings that have a door of the same type.

For example, if you exit building A via the leftmost door a blue door, then you can enter either building D or building E, and if you exit building A via the rightmost door a green door, then you will enter building H.

Question

If you passed through the fewest buildings possible starting in building A and ending in building C, how many types of doors did you travel through?

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

Closer or Farther

Story

Daniel is playing a game to find treasure buried in a grid of squares. Starting from the square labelled “S”, he can only move one step at a time to a neighbouring square. After each step, Daniel receives a signal indicating whether he is now closer to (C) or farther away from (F) the treasure, where the distance is the minimum number of steps it would take Daniel to reach the treasure from his current location.

Daniel plays this game on the following 4-by-7 grid. His path and the signals he receives after each step are shown.

A description of the diagram follows.

You might notice that Daniel does not always make the best decisions.

Question

In which numbered square is the treasure buried?

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

Trains

Story

A train station is shown. It currently contains seven numbered trains in three numbered depots. The main line is connected to these depots. The main line and each depot can each hold up to three trains.

A description of the diagram follows.

Two types of commands result in trains moving between the depots and the main line:

For example, the sequence of commands OUT(3) - OUT(1) - IN(3) - IN(1) will result in trains 5 and 6 exchanging positions.

Question

Which of the following sequences of commands will result in Depot 1 containing trains 1, 2, and 3?

  1. OUT(1) - OUT(2) - IN(1) - OUT(2) - OUT(2) - IN(1) - OUT(3)
  2. OUT(1) - OUT(2) - IN(1) - OUT(2) - OUT(2) - IN(1) - OUT(3) - IN(2) - OUT(3) - IN(1)
  3. OUT(1) - OUT(2) - IN(1) - OUT(2) - IN(1) - OUT(3) - IN(2) - OUT(3) - IN(1)
  4. OUT(1) - OUT(2) - IN(1) - OUT(2) - OUT(2) - IN(1) - OUT(3) - OUT(3) - IN(1)

Watercolour

Story

A beaver designs mazes on rectangular grids of squares. To make the mazes more interesting, it can pour watercolour on a square. The colour then spreads. Every second, colour reaches each uncoloured square that shares an edge with a coloured square. However, colour does not spread through walls. Here is an example:

A grid with 3 rows and 4 columns. There is a vertical wall along the right sides of the bottom two squares in the first column and a horizontal wall along the top sides of the two middle squares in the bottom row. The second square in the middle row is coloured and the remaining squares are uncoloured. The second square in the top row and the second and third squares in the middle row are coloured. The first three squares in the top row and the last three squares in the middle row are coloured. All squares in the top and middle rows are coloured, as is the last square in the bottom row. There are three uncoloured squares remaining.

If different colours are used and poured into two different squares, then the first colour that spreads to an uncoloured square will fill it completely and no new colour will be added. If two colours reach a square at the same time, the square takes the darker colour.

The same 3 by 4 grid with a vertical wall and a horizontal wall. The first square in the top row is coloured dark blue. The last square in the middle row is coloured light pink. The remaining squares are uncoloured. The first two squares in the top row and the first square in the middle row are dark blue. The last square in the top row, the last two squares in the middle row, and the last square in the bottom row are light pink. The first three squares in the top row, the first two squares in the middle row, and the first square in the bottom row are dark blue. The last square in the top row, the last two squares in the middle row, and the last two squares in the bottom row are light pink. There are no new dark blue squares. The second square in the bottom row is now light pink and there are no uncoloured squares remaining.

Question

If different colours are poured as shown, what will the maze look like when the maze is filled with colour?

An alternative format for the diagram follows.


  1. 21 squares are coloured light pink and the remaining 27 are dark blue. The following squares are pink: the first five squares in each of rows 3, 4, 5, and 6, along with the sixth square in row 4.

  2. 21 squares are coloured light pink and the remaining 27 are dark blue. The following squares are pink: the first five squares in each of rows 4, 5, and 6, along with the first, second, fifth, and sixth squares in row 3 and the sixth and seventh squares in row 4.

  3. 26 squares are coloured light pink and the remaining 22 are dark blue. The following squares are pink: all squares in rows 4, 5 and 6, along with the first two squares in row 3.

  4. 18 squares are coloured light pink and the remaining 30 are dark blue. The following squares are pink: the first five squares in each of rows 4, 5, and 6, along with the first two squares in row 3 and the sixth square in row 4.

Companion Planting

Story

Thalia is planting a garden with garlic , tomatoes , sunflowers , corn , and beans .

She wants the plants to help each other grow and knows that some pairs of plants are good companions and some pairs of plants are bad companions:

Good Companions

Bad Companions

All other pairs of plants do not affect each other’s growth.

There are 15 sections in Thalia’s garden bed. She wants to place three of each type of plant in her garden. She has already placed three garlic plants, one corn plant, and one tomato plant as shown.

A description of the garden bed follows.

Question

In how many different ways can Thalia place the remaining plants so that each plant is next to at least one of its good companions, and no plant is next to any of its bad companions?

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