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2025 Beaver Computing Challenge
(Grade 9 & 10)

Questions

Part A

Scoreboard

Story

Two teams are playing baseball. To keep track of their score, each team uses helmets and a row of hooks. The rightmost hook represents a score of 1 and each other hook represents twice the value of the hook to its right, as shown.

Six hooks in row. Starting at the rightmost hook and moving left, the hooks are labelled with the numbers 1, 2, 4, 8, 16, and 32.

Each hook can have at most 1 helmet, and the total score for a team is the sum of all the scores on the hooks with helmets. For example, the following row of hooks would represent a score of \(16+4=20\).

Starting at the rightmost hook and moving to the left, there is a blue helmet on the third and fifth hooks. The other four hooks are empty.

Question

The final scores for the two teams are shown.

Starting at the rightmost hook and moving to the left, there is a blue helmet on the second, third, and fourth hooks. The other three hooks are empty.

Starting at the rightmost hook and moving to the left, there is an orange helmet on the first and second hooks. The other four hooks are empty.

What is the difference between the two scores?

  1. \(11\)
  2. \(9\)
  3. \(13\)
  4. \(7\)

Chung Cake

Story

Banh Chung is a traditional rice cake dish eaten in Vietnam to celebrate the Lunar New Year. These rice cakes are cut using strings placed on the cake one at a time and in different directions.

Question

In what order were the four strings placed on the rice cake shown below?

Four strings labelled P, Q, R, and S are placed on the cake. String P has strings Q and R on top of it. String Q has no strings on top of it. String R has only string Q on top of it. String S has strings P, Q, and R on top of it.

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

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

Planes

Story

Seven planes are lined up for take-off using a single shared runway. A plane cannot take off if there is a plane waiting directly in front of it.

Three runways merge into a single runway. The top runway has a line up of three planes; in order from front to back, the colours of the planes are light green, then yellow, then dark blue. The middle runway has two planes: pink, then dark green. The bottom runway has two planes: light blue, then purple.

The following table shows the take-off schedule, but some of the planes are missing from the schedule.

Time 10:45 10:52 10:55 10:59 11:03 11:10 11:16
Plane pink plane dark blue plane purple plane

Question

If all the planes take off as scheduled, which plane takes off at 11:03?

  1. yellow plane
  2. light green plane
  3. dark green plane
  4. light blue plane

Favourite Fruit

Story

Apples , bananas and pears are placed in five baskets so that each basket has eight pieces of fruit.

Given any two baskets, Blake always prefers the basket with more apples. If two baskets have the same number of apples, then Blake prefers the basket with more bananas.

Question

Which of the following shows the five baskets ordered from Blake's most preferred to least preferred from left to right?

  1. From left to right the baskets have the following: 5 apples, 0 bananas, and 3 pears; 3 apples, 2 bananas, and 3 pears; 3 apples, 4 bananas, and 1 pear; 2 apples, 4 bananas, and 2 pears; 1 apple, 3 bananas, and 4 pears.
  2. 3 apples, 4 bananas, and 1 pear; 2 apples, 4 bananas, and 2 pears; 1 apple, 3 bananas, and 4 pears; 3 apples, 2 bananas, and 3 pears; 5 apples, 0 bananas, and 3 pears;
  3. 1 apple, 3 bananas, and 4 pears; 3 apples, 2 bananas, and 3 pears; 5 apples, 0 bananas, and 3 pears; 2 apples, 4 bananas, and 2 pears; 3 apples, 4 bananas, and 1 pear;
  4. 5 apples, 0 bananas, and 3 pears; 3 apples, 4 bananas, and 1 pear; 3 apples, 2 bananas, and 3 pears; 2 apples, 4 bananas, and 2 pears; 1 apple, 3 bananas, and 4 pears.

Part B

Beaver Timber

Story

Emil's friends have each recorded different data about all the tree species in a forest. When Emil has a question while hiking in the forest, he knows he can call these friends to find the answer to his question.

Question

Emil has found a leaf. He wants to know if it belongs to a tree species whose wood is suitable for building a beaver lodge. Which of his friends must he call?

  1. Only Ladina
  2. Only Severin and Quirina
  3. Only Severin and Ladina
  4. Severin, Quirina and Ladina

Beaver Island Broadcast

Story

There are 13 villages on Beaver Island connected by roads, as shown.

A description of the diagram follows.

Messages are delivered between villages regularly. After a message is sent from one village, it takes one day to reach its immediate neighbours.

If a village wants to broadcast a message to the entire island, they first send the message to all their immediate neighbours. Then each village who receives the message sends it on to their immediate neighbours the same day. This continues until all villages have received the message.

For example, if Village B broadcasts a message, it takes 1 day to reach Villages A and C, and 2 days to reach villages D and E.

Question

If Village H broadcasts a message, how many days will it take for the message to reach all the villages?

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

Sand Painting

Story

Beavers Andy, Bora, Ciel, and Dona are each making a sand painting. They share eleven numbered jars, each containing a different colour of sand. In the picture, each beaver is holding one of the jars they need for their sand painting, and the clouds above their heads show the other jars they need.

Andy is holding jar 2 and also needs jars 1 and 9. Bora is holding jar 8 and also needs 4, 5, and 7. Ciel is holding jar 5 and also needs 2 and 4. Dona is holding jar 11 and also needs 8, 9, and 10.

Two beavers cannot use the same jar at the same time. Also a beaver cannot start their sand painting until they have all the jars they need. Each beaver waits until all the jars they need are available, then they take them all and do their sand painting. When they are finished they return all their jars so others can use them.

Question

Which beaver does their sand painting last?

  1. Andy
  2. Bora
  3. Ciel
  4. Dona

Parking at the Party

Story

Mia's friends drive to her house to attend parties. Her driveway can fit nine cars parked in three columns with three cars in each column, one behind the other.

When a friend arrives, they park at the front of a column or directly behind another car. A friend cannot leave the party until all the cars behind them in their column have left.

For example, given the six parked cars shown below, Car A must have arrived before both Cars D and F. Also, Car E must leave before Car B.

From front to back, the first column has cars A, D, and F, the second column has cars B and E, and the third column has car C.

Question

For another party, cars arrive in the order

A, B, C, D, E, F, G, H, I

and leave in the order

G, D, F, I, H, C, B, A, E.

Which of the following could have been how these cars parked in Mia's driveway?

  1. From front to back, the first column has cars A, B and C, the second column has cars F, D and G, and the third column has cars E, H and I.
  2. From front to back, the first column has cars A, B and D, the second column has cars C, F and G, and the third column has cars E, H and I.
  3. From front to back, the first column has cars A, B and C, the second column has cars D, H and I, and the third column has cars E, F and G.
  4. From front to back, the first column has cars A, B and C, the second column has cars D, E and F, and the third column has cars G, J and I.

Dure

Story

Villagers follow a Korean agricultural cooperative tradition called dure.

The villagers need to choose three dure farming days per week, according to the following rules:

  1. Each dure farming day must have at least four villagers participating.

  2. Each villager must participate in at least one dure farming day per week.

  3. No villager can participate in all three dure farming days in a week.

In the following table, each villager has put a checkmark (✓) under the days they're available for dure.

Name Mon Tue Wed Thu Fri Sat Sun
Ain ✓ ✓ ✓ ✓
Boa ✓ ✓ ✓
Chaewon ✓ ✓
Doyun ✓ ✓ ✓
Eunwoo ✓ ✓ ✓
Felix ✓ ✓ ✓
Gaon ✓ ✓ ✓
Hana ✓ ✓ ✓

Question

Which days should the villagers choose for their dure farming days?

  1. Monday, Tuesday, Wednesday
  2. Monday, Tuesday, Saturday
  3. Tuesday, Wednesday, Thursday
  4. Tuesday, Wednesday, Saturday

Part C

Lights

Story

Sofia has 15 programmable lights of three types: red, blue, and green. She numbers them from 1 to 15 and connects them in a star shape as shown.

A description of the diagram follows.

Each red light is controlled with a switch and Sofia programs the other lights as follows:

Question

All the lights are off and then Sofia turns on lights 1, 2, and 4 at the same time. Which of the five lights closest to the centre (lights 11, 12, 13, 14, and 15) will turn on?

  1. Lights 11, 12, 13, 14, and 15
  2. Only lights 12, 13, and 15
  3. Only lights 11, 12, 13, and 14
  4. Only lights 11, 13, and 14

Mosaic

Story

The arrangement below uses light blue and dark grey shapes. Each shape has 3, 4, 5, or 6 outer points.

blue five-pointed star grey triangle blue hexagon grey square grey hexagon
blue hexagon grey triangle grey triangle grey hexagon grey five-pointed star
blue square blue hexagon grey triangle grey five-pointed star blue triangle
grey five-pointed star grey hexagon blue square blue hexagon blue hexagon
grey triangle grey five-pointed star grey hexagon blue five-pointed star blue triangle

A grumpy beaver didn't like the arrangement above. So, at two locations it removed the shape and then replaced it with a different shape. After doing this, every row and every column had:

Question

Which of the following two new shapes might the beaver have used?

  1. grey triangle and grey hexagon
  2. blue hexagon and grey hexagon
  3. blue five-pointed star and blue square
  4. blue five-pointed star and grey triangle

Third Game

Story

Beavers Anna and Bento are playing a two-player game called Third. The game is played on a \(3\times3\) board using a total of eight pieces. Each piece has three defining attributes: shape (square or circle), colour (grey or white), and marking (diamond or plain). The eight pieces are shown.

White square, white square with a diamond, grey square, grey square with a diamond, white circle, white circle with a diamond, grey circle, grey circle with a diamond.

The game begins with an empty board. The two players take turns placing pieces on the board, however, each piece is selected by their opponent (from the pieces not currently on the board). The player then places this piece on any available square on the board. The winner is the first player to place the third piece in a row or a column so that all three pieces have the same colour, shape, or marking.

For example, suppose the game board is as shown, and Bento chooses the white circle piece for Anna. If she places this piece in the bottom-left corner, then she will win the game because she will have placed the third piece in a column with all circles.

A game board with three pieces placed: the white circle with a diamond is in the top-left square, the grey circle is in the leftmost square in the middle row, and the grey square is in the rightmost square in the middle row. Then, the circle piece is added to the bottom-left square and the first column of the grid is highlighted.

Question

Bento and Anna are playing Third and after each player has placed two pieces, the board is as shown.

A game board with four pieces placed: the grey circle is in the top-left square, the white circle is in the top-right square, the grey square is in the leftmost square in the middle row, and the white circle with a diamond is in the middle square in the bottom row.

It is now Bento's turn. How many of the following four pieces could Anna select for Bento if she wants to ensure that Bento cannot win the game on his turn?

white square with a diamond white square grey circle with a diamond grey square with a diamond

  1. 0
  2. 1
  3. 2
  4. 3

Describing Sequences

Story

Sarah has a very specific procedure for describing sequences of black and white squares:

Below are four examples of sequences and what Sarah writes to describe each of them using her procedure.

Sequence Description
A sequence of 8 white squares. \(\text{W}\)
A sequence of 4 white squares followed by 4 black squares. \(\text{XWB}\)
A sequence of 2 black squares, then 2 white squares, then 4 black squares. \(\text{XXBWB}\)
A sequence of 4 black squares, then 2 white squares, then 1 black square, then 1 white square. \(\text{XBXWXBW}\)

Question

What does Sarah write when using her procedure to describe the following sequence?

A sequence of 8 squares: 1 white square, then 1 black square, then 2 white squares, then 3 black squares, then 1 white square.

  1. \(\text{XXXWBWXBXBW}\)
  2. \(\text{XXXWBXWWXXBBXBW}\)
  3. \(\text{XWBWXBBW}\)
  4. \(\text{XXXBWBXWXWB}\)

Public Transport

Story

Marcus wants to go from his home to the theatre by bus. The following map shows Marcus's home, the theatre, and four bus lines with circles representing bus stops.

Each bus departs from the top of the map. The first bus on each of the four lines departs at the same time. After that, buses depart on each line at the time intervals shown in the squares. For example, a bus departs on the orange line leaving Marcus's home every 3 minutes.

Each line segment between two bus stops is labeled with the number of minutes it takes to travel between the two stops. For simplicity, assume that stopping at a bus stop to load and unload passengers takes no time (0 minutes).

Stops with two or more bus lines intersecting can be used to change buses. If Marcus arrives at an intersection point, he can change to a bus that arrives there at the same time or later.

Question

If Marcus departs on the first bus closest to his home, what is the shortest time, in minutes, needed for him to reach the theatre?

  1. 18
  2. 19
  3. 20
  4. 21