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2022 Beaver Computing Challenge
(Grade 7 & 8)

Questions

Part A

Pick Up Sticks

Story

Ana drops six sticks on a table as shown.

A description of the sticks can be found at the end of the Story.

Then she picks all the sticks up according to the following rules:

  1. Pick up one stick at a time.

  2. Only pick up a stick if no other stick is on top of it.

Question

In which order did Ana pick up the sticks?

  1. solid white, dotted grey, dotted black, solid black, solid grey, dotted white
  2. solid black, dotted grey, dotted white, dotted black, solid white, solid grey
  3. dotted grey, solid white, dotted black, solid grey, solid black, dotted white
  4. dotted grey, solid white, solid black, dotted black, dotted white, solid grey

Missing Library Book

Story

Bibako has left a book somewhere in their house. The picture below is a map of the house. They begin searching for the book in the room marked START. Each of the other rooms is marked with a picture.

A description of the map can be found at the end of the Story.

Bibako moves around the house from room to room until they find the book. Their movements, in order, are represented by the sequence of arrows below. Each arrow represents a move from Bibako’s current location to an adjacent room indicated by the direction of the arrow.

Each arrow points either up, down, left or right. The sequence of arrows is as follows: down, left, left, right, up, up, right, down, right, right.

Question

Which picture corresponds to the room where the book is found?

  1. heart
  2. triangle
  3. sun
  4. lightning

Secret Message

Story

Beavers send messages to each other using sequences of only 0s and 1s. In this system, each letter of the alphabet has its own code. Here are some letters and their codes:

A \(\rightarrow 110\)

B \(\rightarrow 111\)

E \(\rightarrow 10\)

S \(\rightarrow 0\)

The letters of a message are each replaced by their code and the result is 0101011111000.

Question

What was the message?

  1. SEEBASE
  2. SEEBASS
  3. SEEBESS
  4. SEEBEES

Remembering Faces

Story

Talia is very forgetful, so she has created a system to help her remember the names of her four group members.

If a group member is wearing sunglasses, Talia checks to see if they are wearing a hat. If they are wearing a hat, then it is Ash, otherwise it is Deniz. If the group member is not wearing sunglasses, Talia checks to see if they are wearing a scarf. If they are wearing a scarf, then it is Raul, otherwise it is Ming.

A decision tree.

Question

Which of the following correctly matches names with faces?

  1. Ash is wearing sunglasses and a hat. Deniz is wearing sunglasses. Raul is wearing a scarf. Ming is not wearing any of the items.
  2. Ash is wearing sunglasses and a hat. Deniz is wearing sunglasses. Raul is not wearing any of the items. Ming is wearing a scarf.
  3. Ash is wearing sunglasses. Deniz is not wearing any of the items. Raul is wearing a scarf. Ming is wearing sunglasses and a hat.
  4. Ash is wearing sunglasses and a hat. Deniz is wearing a scarf. Raul is wearing sunglasses. Ming is not wearing any of the items.

Target Practice

Story

Maryam is shooting arrows at the target shown. The number in a ring indicates how many points Maryam scores if an arrow hits that ring.

There are six rings labelled with the following numbers: 1, 2, 4, 8, 16, 32.

Maryam shoots three arrows and they all hit different rings.

Question

Which total score is not possible for Maryam to obtain?

  1. 56 points
  2. 21 points
  3. 10 points
  4. 7 points

Part B

Building Instruction

Story

In Beaverland, houses are built out of different blocks. A crane takes blocks one by one in a given order. It puts each block either on the base or on top of another block.

For example, using the block sequence A square block with an X drawn on it, then a square block with a square drawn on it, then a square block with an X drawn on it, then a square block with a triangle drawn on it, the following block house can be built.

The base has two piles of blocks on it. The right pile has one block: a block with an X. The left pile has three blocks: bottom block with a square, middle block with an X, and top block with a triangle.

Question

Which house cannot be built out of the following block sequence?

A long trapezoidal block, then a square block with a triangle drawn on it, then a square block with a drawn square on it, then a square block with an drawn X on it, then another square block with an X on it, then a triangular block.

  1. The long trapezoidal block is on top of the base and two piles of blocks are on top of this. The right pile has three square blocks: bottom block has a triangle on it, middle block has a square on it, top block has an X on it. The left pile has two blocks: bottom block is a square block with an X on it, top block is triangular.
  2. The long trapezoidal block is on top of the base and two piles of blocks are on top of this. The right pile has three blocks: bottom two blocks are square blocks with Xs on them, top block is triangular. The left pile has two square blocks: bottom block has a triangle on it, top block has a square on it.
  3. The long trapezoidal block is on top of the base and two piles of blocks are on top of this. The right pile has three square blocks: bottom block has a triangle on it, top two blocks have Xs on them. The left pile has two blocks: bottom block is a square block with a square on it, top block is triangular.
  4. The long trapezoidal block is on top of the base and two piles of blocks are on top of this. The right pile has two square blocks: bottom block has an X on it, top block has a square on it. The left pile has three blocks: bottom block is a square block with a triangle on it, middle block is a square block with an X on it, top block is triangular.

Nuts and Bolts

Story

At the Beaver Construction Factory, Lana works on the nuts and bolts assembly line.

Her job description is as follows:

However, things can go wrong for Lana in two different ways:

  1. Lana takes a bolt from the conveyor belt, and there is no nut in the bucket to attach it to.

  2. There are no more bolts on the conveyor belt, and there are still nuts in the bucket.

Question

Which sequence of nuts and bolts, when processed from left-to-right, will not cause things to go wrong for Lana?

  1. 1 nut, 2 bolts, 4 nuts, 3 bolts
  2. 2 nuts, 1 bolt, 2 nuts, 4 bolts, 1 nut
  3. 1 nut, 1 bolt, 2 nuts, 1 bolt, 2 nuts, 3 bolts
  4. 2 nuts, 2 bolts, 1 nut, 1 bolt, 3 nuts, 1 bolt

Lights On

Story

Beaver Sofia and her friends are playing an arcade game called "Lights On". The game has 8 buttons for the beavers to stand on. Standing on a button will send a signal down a wire. These wires pass through some triangle or square boxes and eventually lead to a light bulb, as shown.

A description of the diagram follows.

A triangle box will send on a signal if it receives signals from both incoming wires.

A square box will send on a signal if it receives a signal from exactly one of the incoming wires (in other words, from one of the incoming wires but not the other incoming wire).

The beavers win the game if they can turn the light on.

Question

Which of the following combinations of buttons could the beavers stand on in order to win the game?

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

Embroidery Machine

Story

Benoit has a machine which can embroider two kinds of stitches: A vertical stitch and a horizontal stitch that together form a plus sign. and Two diagonal stitches that together form an X.. The machine can also move the fabric by the width of one stitch so that stitches are embroidered from left to right.

If the two kinds of stitches are embroidered (in either order) without moving the fabric, the result is: A six-pointed star made up of a vertical stitch, a horizontal stitch, and two diagonal stitches..

The machine can be programmed using the characters +, x, and > in some sequence.

The machine repeats the entered program some number of times. For example, the program

+ > + x > x >

can cause the machine to embroider:

A pattern of stitches that starts with a plus sign stitch, a star stitch, and an X stitch, and then repeats this three stitch pattern over and over again.

Question

What program can cause the machine to embroider the following?

A pattern of 20 stitches. The stitch types, in order, are X, X, star, X, star, X, X, star, X, star, X, X, star, X, star, X, X, star, X, star.

  1. x > x > x + > x > + x > x > x >
  2. x > x > x + > x > x >
  3. x > x > x + > x > + x >
  4. + x > + x > x > + x > x >

Talking Tiles

Story

Terry lives in a terrific town that is built on top of talking tiles. Each tile contains either a house, trees, grass, or stone.

Terry is visually impaired and so he uses the talking tiles to help him navigate. When he steps onto a tile, the talking tile tells him what is found in the four squares surrounding him in the following order: north (\(\uparrow\)), east (\(\rightarrow\)), south (\(\downarrow\)), and west (\(\leftarrow\)).

Below is a map of the town.

An alternative format of the map follows.

Terry is currently standing on the stone tile marked with a star. When he stepped onto this tile, the talking tile said "trees stone house stone".

Terry decides to go for a walk around town and hears the following as he walks:

Terry only walks north, east, south and west.

Question

Where is Terry now?

  1. heart symbol
  2. diamond symbol
  3. club symbol
  4. spade symbol

Part C

Signal Lamps

Story

At a small seaside cafe, Bombom takes food orders and Lala does all the cooking. To send food orders to Lala, Bombom uses two signal lamps; one shaped like a leaf, and the other shaped like a flower. At first the cafe sold only coffee and tea and they assigned each item the following codes.

Item Code
coffee leaf leaf
tea leaf leaf flower

This caused a problem, however, because Lala starts to prepare each drink as soon as she receives a complete code, instead of waiting to see if Bombom is finished. So whenever Bombom turns on the leaf lamp twice, Lala does not wait to see if another signal is sent. Instead, she starts to prepare a coffee, since the complete code for coffee (two leaves) has been sent.

They expanded their menu and assigned new codes to avoid any problems like this. The new menu and codes are as follows.

Item Code
coffee leaf leaf
tea leaf flower leaf flower
juice flower leaf
sandwich leaf flower flower
muffin flower flower flower

Question

If they decide to add pie to the menu, which new code can be used without causing any problems?

  1. flower flower leaf
  2. leaf leaf flower
  3. leaf flower leaf
  4. flower flower flower leaf

Beach Necklaces

Story

Bashir makes necklaces using wavy beads and blue beads. He always makes them as follows.

  1. Place one wavy bead and one blue bead on a string with the wavy bead to the left of the blue bead.

  2. Do one of the following two actions.

    Starting with a string with a wavy bead on the left and a blue bead on the right, applying action B results in a string with the following beads from left to right: blue, wavy, blue, blue. If instead action W is applied, the result is a string with the following beads: wavy, blue, wavy, wavy.

  3. Repeat step 2 until the necklace is complete.

Question

Which necklace below cannot be made by Bashir?

  1. From left to right the beads are 1 blue, 1 wavy, 2 blue, 4 wavy.
  2. From left to right the beads are 2 blue, 1 wavy, 3 blue, 2 wavy.
  3. From left to right the beads are 1 blue, 1 wavy, 1 blue, 2 wavy, 1 blue, 2 wavy.
  4. From left to right the beads are 1 blue, 1 wavy, 3 blue, 3 wavy.

Beautiful Gems

Story

Troy has a collection of gems. He ranks his gems from most beautiful to least beautiful.

Sarah knows what gems are in Troy’s collection, but she does not know how he has ranked them.

Sarah has a strategy to find out which gem is most beautiful according to Troy:

When Sarah chooses her second and third set of four gems, she may sometimes include gems she has chosen before. Troy answers each question honestly and Sarah remembers all of Troy’s answers.

Sarah’s strategy allows her to find the most beautiful gem according to Troy, regardless of his ranking.

Question

What is the largest possible number of gems in Troy’s collection?

  1. 8
  2. 10
  3. 11
  4. 12

Connected Islands

Story

A community spread across six islands must connect all the islands together by building bridges. A map of all the possible bridges and the cost of building each bridge is shown.

A description of the map can be found at the end of the Story.

The community needs it to be possible to travel from any island to any other island either directly or indirectly.

Note that when you are on a bridge, you can only leave the bridge where it ends at an island. For example, you cannot hop between the bridges that cost 10 and 13 even though they overlap.

Question

What is the lowest possible total amount that the community can spend on bridges?

  1. 46
  2. 45
  3. 44
  4. 40

Mysteria

Story

The inhabitants of Mysteria can be wizards, fairies, potions, or dragons. They always arrange themselves in a row and can undergo four types of magical transformations:

  1. A wizard can turn into a fairy
      \(\rightarrow\)  

  2. A wizard can turn into a wizard (on the left) and a fairy beside them (on the right)   \(\rightarrow\)  

  3. A fairy can turn into a potion (on the left) and a dragon (on the right)
      \(\rightarrow\)  

  4. A fairy can turn into a wizard, with a potion beside them (on the left) and a dragon beside them (on the right)
      \(\rightarrow\)    

These magical transformations can happen any number of times, in any order. That is, any wizard and any fairy in Mysteria can transform at any time.

Question

Starting with the single wizard, which state of Mysteria is not possible to obtain?

  1. potion wizard potion dragon dragon
  2. wizard potion fairy dragon potion fairy potion dragon
  3. fairy potion dragon potion wizard dragon
  4. potion dragon potion dragon