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2021 Beaver Computing Challenge
(Grade 5 & 6)

Questions

Part A

Strawberry

Story

Anja makes a design on the ground using the following four types of objects.

acorn hazelnut stone strawberry

She then places sticks in her design according to her very important rule:

Sticks cannot be placed between objects that are the same type.

Here is Anja’s completed design:

Six of the objects are placed in two rows of three. The first row consists of an acorn, a hazelnut, and another acorn. The second row consists of a stone, a strawberry, and a stone. Sticks connect the strawberry in the second row with all objects in the first row, and every other object in the second row.

Suddenly a bird swoops in and eats the strawberry ! Anja would like to avoid having this happen again.

Question

If possible, Anja would like to replace the strawberry with a different type of object, and without moving any sticks. Without breaking her very important rule, which object can Anja replace the strawberry with?

  1. an acorn
  2. a hazelnut
  3. a stone
  4. It is not possible. Only a strawberry could go there.

Overlapping Coins

Story

Emil has six different coins.

Emil placed the six coins on a table, one at a time. Some coins were placed on top of other coins so that they overlap as shown.

Coins A, B, C, D, E, and F are placed in a pile in three levels. Coin D is on the bottom level. Coins C and F are on top of Coin D in the middle level, with Coin C on top of Coin F. Coins A, B and E are on the top level, with coin E on top of Coin B and Coin A on top of Coin E.

Question

Which coin was the fourth coin that Emil placed on the table?

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

Robot Arm

Story

There are three bins, two balls, and a robot arm that can pick up the balls. Originally, one ball is in bin A and another is in bin B. Bin C is empty.

A black ball is in bin A, a green ball is in bin B, and bin C is empty.

Then the robot arm completes the following steps in the order given:

  1. Pick up the ball in bin A and put it in bin C.
  2. Pick up the ball in bin B and put it in bin A.
  3. Pick up the ball in bin C and put it in bin B.

Question

When the robot arm is finished, which of the following statements is true?

  1. The ball originally in bin A is now in bin B, and the ball originally in bin B is now in bin A.
  2. Both balls are in bin A.
  3. Bin A is empty.
  4. Nothing has changed. Each ball is back in its original bin.

Fruit Road

Story

A beaver wants to take a path to the river. Each path passes by three different types of fruit as shown.

A description of the diagram follows.

The beaver must pass by a pineapple which is its favourite fruit.

The beaver must not pass by an orange which it is allergic to.

Question

How many of the eight possible paths can the beaver take?

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

Part B

Picking Up Carrots

Story

There are 5 animal homes connected by paths with a carrot on each path, as shown.

There are five houses labelled P, Q, R, S, and T. There are seven different paths, each with a carrot. Four paths connect house P to each of the other four houses. The three other paths connect R to S, Q to S, and S to T.

Rina Rabbit lives in house R. It takes Rina 1 minute to walk on any path between two homes.

Question

Which of the following routes allows Rina to pick up all the carrots and return home in the shortest amount of time?

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

Presents

Story

Friends give presents to one another according to the following two rules.

  1. Each friend must give exactly one present.
  2. Each friend must receive exactly one present.

Here is an example where Cat gives a present to Mouse, and Mouse gives a present to Cat:

Question

Cow, Cat, Dog and Mouse give presents to each other. Which of the following options does not follow the rules?

  1. Cat gives to Cow. Dog gives to Cat. Mouse gives to Dog. Cow gives to Mouse.
  2. Cow gives to Mouse. Cat gives to Dog. Dog gives to Cat. Mouse gives to Cow.
  3. Mouse gives to Cat. Cow gives to Dog. Cow gives to Mouse. Cat gives to Dog.
  4. Cow gives to Dog. Mouse gives to Cow. Cat gives to Mouse. Dog gives to Cat.

Coin Bag

Story

In Saoirse’s country there are four different types of coins. Some coins are the same on both sides, and some are not. The images below show both sides of each type of coin.

A coin with one green side and one yellow side. A coin with one red side and one blue side. A coin two identical orange sides. A coin with two identical purple sides.

Saoirse has the following bag of coins:

One side of each of eight coins is visible. One coin shows a red side, one shows an orange side, one shows a yellow side, three show green sides, one shows a blue side, and one shows a purple side.

Then the bag is shaken and the coins in the bag move around.

Question

Which of the following could be Saoirse’s bag of coins after it was shaken?

  1. A bag showing one red, one orange, two yellow, one green, two blue, and one purple side.
  2. A bag showing two orange, one yellow, three green, one blue, and one purple side.
  3. A bag showing two red, one orange, two yellow, two green, and one purple side.
  4. A bag showing two red, one orange, two green, two blue, and one purple side.

Necklaces

Story

A jeweller makes necklaces with hidden messages by replacing each letter of the alphabet with a bead pattern. Bead patterns are made using heart and diamond beads, and the same bead pattern always represents the same letter. Letters in a message are separated by oval beads and messages are read from left to right.
Here are two of the necklaces the jeweller has made along with their hidden messages.

Necklace Hidden Message
From left to right, the beads are: a diamond, an oval, a heart, a diamond, a heart, an oval, two hearts, a diamond, an oval, a diamond, an oval, four hearts. TRUTH
A diamond, a heart, a diamond, a heart, an oval, a heart, a diamond, an oval, a heart, a diamond, a heart, an oval, a heart. CARE

Question

Which of the following necklaces has the hidden message ART?

  1. A diamond, a heart, a diamond, a heart, an oval, a heart, a diamond, an oval, a diamond.
  2. A heart, a diamond, an oval, a heart, a diamond, a heart, an oval, a heart.
  3. A diamond, an oval, a heart, a diamond, an oval, a heart, a diamond, a heart.
  4. A heart, a diamond, an oval, a heart, a diamond, a heart, an oval, a diamond.

Part C

Do They Meet?

Story

On Lake Castor, lilypads are arranged in a grid, where rows are numbered from 1 to 5, and columns are labelled from A to H. Beaver Bob starts on pad A1 (in the bottom-left corner), and Beaver Nora starts on pad H3.

An alternative format for the grid follows.

The beavers can move from one lilypad to another lilypad only if they are following an arrow. The beavers do not necessarily move at the same speed.

Question

Which of the following statements is true?

  1. The beavers will never meet.
  2. The beavers could meet on pad C2.
  3. The beavers could meet on pad F4.
  4. The beavers could meet on pad C5.

Paintings

Story

Paintings are brought to a warehouse for inspection before they are delivered to museums. The paintings are stacked on top of each other. When a painting arrives at the warehouse, it is put on top of the stack. When a delivery person departs with a painting, they take the painting from the top of the stack.

Records are kept of all paintings arriving at the warehouse and departing from the warehouse:

Arrivals
Time Painting
11:40 Beavers on the Grass
12:15 Happy Beaver
12:55 Sun and Moon
13:30 Enchanted Forest
14:18 Oak and Birch
Departures
Time Delivery Person
12:25 Pia
13:35 Raz
14:35 Stu
14:40 Quy
15:20 Raz

Question

Which delivery person took “Sun and Moon” to a museum?

  1. Pia
  2. Quy
  3. Raz
  4. Stu

Shapes

Story

Here is a line of shapes.

The line has nine shapes of four different types. From left to right, the shape types are triangle, square, circle, star, square, star, star, circle, square.

The line has a run of stars of length 2. A run is an unbroken chain of identical shapes.

Ali likes to create long runs by changing shapes. For example, if Ali changes the middle square to a star in the line above, then he can create a longer run of length 4.

Question

Suppose Ali chooses and changes exactly 3 of the 16 shapes in the following line:

From left to right, the shapes types are circle, star, circle, square, triangle, star, circle, triangle, square, triangle, star, square, sircle, triangle, star, square.

What is the length of the longest possible run that Ali can create?

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

Upcycling

Story

Doreen uses old things as supplies to make new items; this is called upcycling. Doreen upcycles her supplies into wheels, bicycles, and tricycles, then sells her new items at the market. The supplies needed to make each new item are shown in the table.

Supplies Needed New Item

Tire     +    Iron Bar
Wheel

2 Wheels   +   Iron Bar
Bicycle

Bicycle    +    Wheel
Tricycle

Question

Doreen has 9 tires and 11 iron bars. What is the maximum number of tricycles she can make?

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