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2016 Beaver Computing Challenge
(Grade 7 & 8)

Questions

Part A

Boxes

Story

Boxes are shown below. Each box is labeled with its mass in kilograms.

Five boxes labelled with 1, 2, 4, 8 and 16.

Xena the delivery beaver fills out a form to order boxes. For example, to order boxes totalling exactly 9 kilograms, she fills out the form as follows:

✓ ✓
16 8 4 2 1

Question

How should she fill out the form to order boxes totaling exactly 20 kilograms?

  1. ✓ ✓ ✓
    16 8 4 2 1
  2. ✓ ✓
    16 8 4 2 1
  3. ✓ ✓
    16 8 4 2 1
  4. ✓ ✓ ✓ ✓
    16 8 4 2 1

Secret Recipe

Story

Beavers are preparing for a Food Festival. They would like to bake a cake but their baker is on vacation.

Keith decides to try to bake the cake. He remembers that it is important to add five essential ingredients in the correct order.

When he gets to the garden shown below, he finds a white piece of paper beside all but one ingredient. The paper shows which ingredient must be added next.

A description of the garden follows.

So, for example, a yellow five-petal flower must be added immediately after a pine cone. And, since there is no paper beside the strawberry, it must be added last.

Question

Which ingredient must be added first?

  1. strawberry
  2. red four-petal flower
  3. apple
  4. pine cone

Shaman Pictures

Story

An artist painted several images of a shaman. In her favourite image, the shaman

Question

Which image is her favourite painting?

  1. The shaman has a parrot in his left hand, does not hold a stick, and not all buttons on his coat are buttoned.
  2. The shaman has a parrot in his right hand, does not hold a stick, and all buttons on his coat are buttoned.
  3. The shaman has a parrot in his left hand, holds a stick, and all buttons on his coat are buttoned.
  4. The shaman has a parrot in his left hand, does not hold a stick, and all buttons on his coat are buttoned.

Pond Planning

Story

Beaver neighbourhoods consist of rivers flowing between ponds. Patricia is grumpy and wants to build one dam in each neighbourhood that will cause trouble. That is, she wants to block a single river so that beavers will not be able to travel between all pairs of ponds in the neighbourhood.

Question

In which of the following neighbourhoods is Patricia unable to build her dam?

  1. Neighbourhood A has five ponds where some ponds are connected by rivers and no rivers intersect. Rivers flow between ponds 1 and 2, 2 and 4, 4 and 3, and 1 and 3. Rivers also flow between pond 5 and each of ponds 2, 3, and 4.
  2. Neighbourhood B has seven ponds where some ponds are connected by rivers and no rivers intersect. Rivers flow between ponds 1 and 2, 2 and 3, 3 and 4, and between ponds 1 and 4. A river flows between ponds 3 and 5, 5 and 6, 6 and 7 as well as between ponds 5 and 7.
  3. Neighbourhood C has four ponds where some ponds are connected by rivers and no rivers intersect. Rivers flow between ponds 1 and 2, 2 and 3, 3 and 4, as well as between ponds 2 and 4.
  4. Neighbourhood D has eight ponds where some ponds are connected by rivers and no rivers intersect. Rivers flow from pond 1 to each of ponds 2, 4, and 6. Rivers flow between ponds 2 and 3, ponds 3 and 4, ponds 4 and 5, ponds 6 and 7, ponds 7 and 8, and ponds 6 and 8.

Party Banner

Story

You have a long roll of coloured paper for a party you are hosting. The paper consists of the following pattern repeated more than once:

A rectangular piece of paper is divided into four sections of equal length. The sections, from left to right, are coloured yellow (Y), red (R), red (R), blue (B).

A beaver cut out a section of the paper between pieces of length 11 and 6 as shown below.

11 sections are coloured Y,R,R,B,Y,R,R,B,Y,R,R(...paper cut out by beaver...)6 sections are coloured R,B,Y,R,R,B.

Question

Which of the following can be the length of the paper cut out by the beaver?

  1. 31
  2. 32
  3. 33
  4. 34

Part B

Firefighter

Story

The mayor of Beaverville is looking for volunteer firefighters. A map showing the possible volunteers’ homes and how they are connected by roads is shown below. He wants to ensure that every home in the town is either the home of a volunteer or is connected by a single road to the home of a volunteer.

9 homes are connected by 10 roads. Each road connects 2 homes together. Bob is connected to Ann, Cid and Dan. Hal is connected to Dan, Gus and Ian. Eve is connected to Cid and Ian, and Fay is connected to Cid and Ian.

Question

What is the minimum number of volunteers the mayor needs?

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

Propagate

Story

Roberta Beaver has purchased an old computer that only allows one digit after the decimal point in any calculation. Anything after that digit is removed. Sometimes this results in an error which is the difference between the stored value and the exact value.

For example, if we try to compute \(\frac{7}{5}\) on Roberta’s machine, this will be stored as \(1.4\) which is the exact value of \(\frac{7}{5}\). This gives an error of 0. However, if we compute \(\frac{7}{4}\), this will be stored as \(1.7\) since \(\frac{7}{4}=1.75\) and “\(5\)” will be removed from the end. This gives an error of \(0.05\).

Extra digits are removed after every operation. For example, when Roberta computes \(\left({\frac{3}{2}}\right)\times\left(\frac{2}{3}\right)\), she computes \(\frac{3}{2}\) to give \(1.5\), then \(\frac{2}{3}\) to give \(0.6\), and then \(1.5 \times 0.6\) to give \(0.9\). This gives an error of \(0.1\).

Question

If Roberta computes \(\left(\left(\frac{10}{3}\right)\times\left(\frac{10}{3}\right)\right)\times 9\), what is the error?

  1. \(0.0\)
  2. \(1.3\)
  3. \(2.8\)
  4. \(3.3\)

Collecting Wood

Story

During his descent from the mountain top, the beaver, Theseas, is collecting wood for his lodge from several stations. Every station holds a different amount of wood. While he is descending, he cannot change direction and start climbing again, that is, he can only go in the directions of the arrows.

The paths between stations are given in the image below. Every circle is a station and the number in the circle represents the amount of wood available at that station.

A description of the diagram follows.

Question

What is the maximum total amount of wood that Theseas can collect during his descent?

  1. 19
  2. 20
  3. 21
  4. 22

Meeting

Story

Five beavers happily live around a circular canal. They decided to have regular meetings at one of their residences. They want to minimize the total swimming distances for them to get to the meeting place.

A circular canal has five residences around it. Starting at Betty's and moving around the circle, it is 400 units to Bobby's, then another 120 to Ben's, then 80 to Bubba's, then 300 to Bart's, and finally 200 back to Betty's.

Question

At whose residence will the meeting take place?

  1. Bobby
  2. Ben
  3. Bubba
  4. Bart

Spherical Robot

Story

The BeaverBall is a toy operated by remote control which can be used to move the toy in four possible directions:

The four directions are North (N), South (S), East (E), and West (W).

The BeaverBall operates inside a tower with its initial position shown below.

A description of the tower follows.

If the BeaverBall moves to a white square, it drops down one level falling directly onto the square below. The BeaverBall ignores commands that cause it to move outside the tower.

Question

Which of the following lists of directions will cause the BeaverBall to reach the GOAL?

  1. E, W, N, W, W
  2. E, W, N, E, S, W
  3. E, W, E, N, S, W
  4. E, N, W, S, N, E, W

Part C

Replacing Shapes

Story

Alice the beaver plays a game with shaped cards. She starts with a single card that is a square and uses the following set of replacement rules.

The result of following these rules three times is shown below.

S to T,T to S,T,S,S,T,S to T,T,S,T,S,T,T,T,T,S,T,S,T,T

Boris the beaver plays a similar game. He starts with one of a square, triangle or circle and he plays with a different set of replacement rules. The result of following these rules three times is shown below.

T,S,S,C,C,S,C,C,S,T,S,T, where C represents a Circle.

Question

Which of the following set of replacement rules might Boris have used?

  1. S to T,S,S, and T to C, and C to T,T 

  2. S to S,C,C, and T to T,S, and C to S,T 

  3. T to T,T, and S to C,C, and C to T,S,T 

  4. T to S,C, and S to T,T,T, and C to S,T

Magic Potions

Story

Betaro Beaver discovered five types of magic potions with the following effects:

Betaro put each magic potion into a different cup and additionally put water into a sixth cup. Betaro labelled the cups A to F and forgot to record which cup contains which magic potion!

Betaro called Taki for help. She solved the problem by experimenting on three of their other friends:

In Figure 1, the effects are longer ears, longer teeth, and a white nose. In Figure 2, the effects are longer ears, and white eyes. In Figure 3, the effects are curly whiskers, and a white nose

Question

Which one of the cups contains pure water?

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

Instachat and Snapgram

Story

Information is given below about the friendships between a beaver, rabbit, hedgehog, squirrel and skunk on the social network Instachat. In the picture, the lines show which animals are friends with each other. The table records how many friends each animal has.

There are lines between the following pairs of animals: Beaver and Rabbit, Beaver and Hedgehog, Beaver and Squirrel, Beaver and Skunk, Rabbit and Hedgehog.

Animal Number of Friends
beaver 4
rabbit 2
hedgehog 2
squirrel 1
skunk 1

Five different animals are on a different social network Snapgram and the same information is recorded in the same way.

Question

Which of the following cannot be the table recording how many friends each animal has on Snapgram?

  1. Animal Number of Friends
    fox 2
    groundhog 2
    chipmunk 2
    turtle 2
    snake 2
  2. Animal Number of Friends
    fox 2
    groundhog 3
    chipmunk 4
    turtle 3
    snake 2
  3. Animal Number of Friends
    fox 1
    groundhog 4
    chipmunk 3
    turtle 4
    snake 1
  4. Animal Number of Friends
    fox 3
    groundhog 3
    chipmunk 4
    turtle 3
    snake 3

Switches

Story

Edward the beaver built a colourful lights display in the center of town. The lights can be made to flash in eight different pretty patterns by turning three switches on and off. Edward wants to test every pattern. To do so, he needs to try all eight different on/off combinations of the three switches. Unfortunately, the switches are each one kilometer apart and Edward has to walk to a switch to be able to change it.

A map of the town with three switches placed with one at each the corners of an equilateral triangle.

Question

If Edward can start at any one of the switches, what is the least number of kilometers he has to walk?

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

L-Game

Story

Kiki and Wiwi are playing L-Game on a 4x4 board. The player who can no longer play a piece loses. They take turns placing L-shaped pieces one at a time with Kiki playing first so that

The diagram below illustrates a possible board after each player has placed a piece once.

A description of the diagram follows.

Question

Starting from an entirely empty board, how many of Kiki’s nine possible first moves guarantee that Kiki will win no matter what?

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