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2020 Beaver Computing Challenge
(Grade 7 & 8)

Questions

Part A

Skyline

Story

A skyline consists of 14 towers as shown. The height of a tower is measured from the bottom of its base to its highest point, including any flagpoles or antennas.

A description the diagram follows.

Question

If the towers are listed from shortest to tallest, which tower would be 10th in the list?

  1. the twelfth tower
  2. the eleventh tower
  3. the sixth tower
  4. the fifth tower

Crypto Keys

Story

Jan uses a special keyboard for writing secret messages. When a key on the keyboard is pressed, a different letter is displayed on the screen, according to the following keyboard map:

A description of the keyboard map follows.

The arrows indicate which letter is displayed when each key is pressed. For example, when Jan presses the “S” key, the letter “E” is displayed on the screen, and when Jan presses the “E” key, the letter “S” is displayed on the screen.

Jan types a message and the letters “QOEU” are displayed on the screen, in that order.

Question

What was the original message typed by Jan?

  1. WASH
  2. WITH
  3. WISP
  4. WISH

Cookies

Story

Four children ask for cookies.

Adam says “I don’t want stripes on my cookie.”

Bella says “I want my cookie to be a circle or a square.”

Cai says “I want a cookie with little round dots.”

Diego says “I want a star-shaped cookie.”

Question

Which of the following assignment of cookies will satisfy all the children’s requests?

  1. Adam Bella Cai Diego
    square cookie with stripes triangle cookie with round dots circle cookie with hearts star cookie with no pattern
  2. Adam Bella Cai Diego
    circle cookie with hearts triangle cookie with round dots square cookie with stripes star cookie with no pattern
  3. Adam Bella Cai Diego
    circle cookie with hearts square cookie with stripes triangle cookie with round dots star cookie with no pattern
  4. Adam Bella Cai Diego
    star cookie with no pattern square cookie with stripes triangle cookie with round dots circle cookie with hearts

Connect the Dots

Story

Zhi likes to draw. He creates his pictures by drawing dots and then connecting them with line segments in one motion, never picking up his pencil and never drawing the same line segment twice.

This is how Zhi draws a picture of a house:

A description of the diagram follows.

Question

Which of the following pictures can Zhi draw?

  1. A picture with 6 dots arranged into two rows and three columns. There are lines connecting the top middle dot to all of the other dots, and also a line connecting the two dots in the third column.
  2. A picture with 6 dots: top-left, top-middle, top-right, centre, bottom-left, and bottom-right. The centre, bottom-left and bottom-right dots are connected forming a triangle; the top middle dot is connected to the top-left, top-right, and centre dots.
  3. A picture with 6 dots. 3 dots are connected forming a triangle pointing down and, below it, the 3 other dots are connected forming a triangle pointing up. The bottom vertex of the top triangle is connected to the top vertex of the bottom triange.
  4. A picture with 7 dots. 4 dots are connected forming a large square and the other 3 dots are connected forming a small triangle inside the square, not touching the square.

Towns and Highways

Story

A map of five towns (black dots) and four highways (coloured lines) is shown.

A description of the map follows.

To represent this map using a diagram, there is one labelled circle per town and the following is true for every two towns:

  1. If you can drive from one town to the other using exactly one of the four highways, then a straight line joins their circles.
  2. If you cannot drive from one town to the other using exactly one of the four highways, then no straight line joins their circles.

Question

Which diagram represents the given map?


  1. Five circles labelled P, Q, R, S, T. Lines join S to each of the other circles, and a line joins R and T.

  2. Five circles labelled P, Q, R, S, T. Lines join S to each of the other circles, a line joins P and Q, and a line joins Q and R.

  3. Five circles labelled P, Q, R, S, T. Lines join S to each of the other circles, and a line joins Q and R.

  4. Five circles labelled P, Q, R, S, T. Lines join S to each of the other circles, and a line joins P and Q.

Part B

Library Books

Story

Beavertown Library has only a small pile of books. When a beaver wishes to borrow a book, they take the book that is on the top of the pile and record their name. When a beaver returns a book, they place their book on the top of the pile and record their name again.

At the beginning of the week the pile of books was arranged as shown:

5 books are stacked in a pile. From top to bottom, the titles of the books are 'Charlotte's Web', 'Curious George', 'Go, Dog, Go!', 'The Hobbit', and 'Fox in Socks'.

The library’s records at the end of the week show the following information:

Six lines, from top to bottom, read: Alba - Borrow, Felix - Borrow, Alba - Return, Marta - Borrow, Felix - Return, Cato - Borrow.

Question

Which book did Cato borrow?

  1. Charlotte’s Web
  2. Curious George
  3. Go, Dog, Go!
  4. The Hobbit

Market Exchange

Story

A beaver goes to a market to trade items. It has one carrot but needs one fir tree .

Each stall of the market allows a different trade as shown:

Stall Give Get
\(P\) carrot fish
\(Q\) coin fish
\(R\) ring cupcake
\(S\) carrot cupcake
\(T\) coin fir tree
\(U\) ring fir tree
\(V\) cupcake ring
\(W\) carrot leaf

Question

Which of the following sequences of stalls should the beaver visit in order to trade its carrot for one fir tree ?

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

House Painting

Story

To brighten up the street Mei lives on, each white house will be painted red (R), green (G) or blue (B).

After all the houses have been painted, the following must be true:

  1. Two houses next to each other must not be the same colour.
  2. A house must not be the same colour as the house directly across the street.

Before painting, these are the houses on Mei’s street:

The street has 5 houses in a row on the north side and one house directly across from each of these five houses on the south side. On the north side, the houses in order are painted red, white, blue, white, and green. On the south side, the houses in order are painted blue, white, white, white, and red. Mei's house is the fourth house on the south side.

Question

Which colour(s) can be used for Mei’s house?

  1. Only red can be used.
  2. Only blue can be used.
  3. Only green can be used.
  4. Either red or green can be used.

Treasure Hunt

Story

Three explorers are working together to find a hidden treasure chest. They each take a different path (upper, middle, or lower) and they explore their paths by running from left to right.

There are several large obstacles blocking their paths.

When an explorer encounters an obstacle, they must wait until it is crumbled before they can proceed. An obstacle is crumbled when one of the explorers steps on a stone that is marked with the same symbol as the obstacle. In fact, stepping on a stone crumbles all obstacles that are marked with the same symbol as the stone.

The obstacles, stones, and explorers are arranged as shown.

A description of the diagram follows.

Question

Which explorer can get to the treasure chest?

  1. Explorer A
  2. Explorer B
  3. Explorer C
  4. No explorer can get to the treasure chest.

Water Bottles

Story

Dani is required to entirely fill as many empty water bottles as possible using a 50 litre tank.

Suppose she is given the following 10 empty bottles where each bottle is labelled with the number of litres it can hold.

The 10 bottles are labelled with 6, 4, 3, 15, 9, 7, 5, 11, 9, and 8.

Question

What is the maximum number of bottles that Dani can fill entirely?

  1. 4
  2. 7
  3. 8
  4. 10

Part C

Spider Car

Story

In the fenced area shown there are yellow cars and a single red spider car.

A description of the diagram follows.

Ayo is trying to get the spider car in the spider square just outside the fenced area.

In one move, Ayo can:

There can only be one car per square at any given time and only the spider car can be moved into the spider square.

Question

What is the minimum number of moves Ayo needs to get the spider car in the spider square?

  1. 9
  2. 11
  3. 13
  4. 15

Puzzle Pieces

Story

A beaver has a puzzle with 12 different types of pieces, 4 of which are red, 4 of which are yellow, and 4 of which are blue, as shown below. There is an unlimited number of each type of piece.

  

A description of the puzzles pieces follows.

Using these pieces, the beaver can create various colour sequences. The first piece in a sequence must have a flat left side and the last piece must have a flat right side. Pieces join in the usual way but two pieces can’t be joined on their flat sides and pieces can’t be rotated. One possible sequence is shown below.

8 pieces joined together in a line. A description of the pieces in order from left to right follows.

Question

Which of the following colour sequences cannot be constructed?

  1. YELLOW \(\rightarrow\) BLUE \(\rightarrow\) BLUE \(\rightarrow\) RED \(\rightarrow\) BLUE
  2. BLUE \(\rightarrow\) YELLOW \(\rightarrow\) RED \(\rightarrow\) YELLOW \(\rightarrow\) RED
  3. RED \(\rightarrow\) RED \(\rightarrow\) YELLOW \(\rightarrow\) BLUE \(\rightarrow\) BLUE
  4. BLUE \(\rightarrow\) RED \(\rightarrow\) YELLOW \(\rightarrow\) BLUE \(\rightarrow\) RED

Spreading the News

Story

Twelve beavers share news with each other using a network of wires as shown:

A description of the diagram follows.

Two beavers can share news if they are directly connected by a wire. For example, beaver 6 is directly connected to beavers 7 and 10 but not to beaver 3.

All beavers want to hear news as quickly as possible. As such, a beaver with news uses all of its wires simultaneously to inform the other beavers that it is directly connected to.

For example, if beaver 8 has news it will inform beavers 1 and 11 right away. Next, beavers 1 and 11 will further spread the news, at the same time, to beavers 2, 4, and 5. The beavers continue to spread the news using their wires until all beavers have been informed.

Question

If there is news that should be spread as quickly as possible, which beaver should be informed of the news first?

  1. 1
  2. 2
  3. 4
  4. 10

Book Organizer

Story

Bora uses a flowchart to organize her books onto three shelves. When she gets a new book, she starts at the top of the flowchart and follows its instructions to determine on which shelf the book belongs.

Each diamond in the flowchart includes a “yes” or “no" question about the book’s title. The answer determines which arrow leading away from the diamond Bora will follow. When an arrow points at a shelf, the book is added to that shelf. Otherwise, Bora continues to move through the flowchart.

A description of the flowchart diagram follows.

Question

If Bora’s books end up on the shelves as shown, which of the following questions could have appeared in the diamond marked with a question mark (?) in the flowchart?

  1. Does the title include the word “Men”?
  2. Are there fewer than four words in the title?
  3. Is the letter “i” in the title?
  4. Does the title include a number?

Train Trip

Story

A train has three carriages, with the number of available seats and luggage limits as shown:

The first carriage has 6 seats and a 160 kg limit. The second carriage has 10 seats and a 200 kg limit. The third carriage has 15 seats and a 300 kg limit.

Eight beaver families would like to go on a train trip, but

Details about each family and their luggage are given in the following table:

Family Number of Members Luggage Weight (kg)
Avsec 3 50
Bizjak 4 80
Cerar 5 110
Dolenc 4 80
Erjavec 2 40
Furlan 3 70
Gabric 6 130
Hacin 5 100

Question

What is the maximum number of families that can go on the trip?

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