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2022 Beaver Computing Challenge
(Grade 9 & 10)

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

Lost In Space

Story

The mission to explore planet Castor was a success, except for the astronauts losing their personal belongings!

A self-driving robot was sent back to Castor in order to collect all the missing items. The robot can only drive north (\(\uparrow\)), south (\(\downarrow\)), east (\(\rightarrow\)), and west (\(\leftarrow\)). The robot is currently located in the first column on the third row and it has detected the location of seven lost items as shown:

A description of the diagram follows.

The robot is programmed to identify the item it can get to by driving through the least number of cells. Then it moves to the cell containing that item, and picks the item up. The robot repeats this program until all detected items have been picked up.

Question

Which item does the robot pick up last?

  1. basketball
  2. scissors
  3. calculator
  4. shoe

Octagon Cipher

Story

In an octagon cipher, groups of letters are placed at each vertex of an octagon. An arrow points from the center of the octagon to a letter group, and the arrow can rotate clockwise.

The arrow points to the letter group ABC. Going clockwise from here, around the octagon, the other letter groups are DEF, GHI, JKLY, MNOZ, PQR, STU, and VWX.

This octagon cipher is used to create secret versions of words. For each word, the arrow begins pointing to ABC. Then a pair of digits is generated for each letter in the word as follows:

The pairs of digits are then separated by dashes. For example, the secret version of the word TREE is 62-73-42-02.

Question

What is the secret version of the word WATER?

  1. 72-11-26-32-53
  2. 62-11-62-22-43
  3. 62-11-26-22-53
  4. 72-11-62-32-43

Colourful Tower

Story

Luis has hexagon pieces in three different colours. Whenever Luis arranges three pieces in a way that resembles an upright triangle, the three pieces must either be all the same colour, or all different colours. These rules do not apply to other three-piece arrangements. In particular:

All colours the same
or all colours different
Three identical regular hexagons placed so they have two vertical sides, two angled top sides, and two angled bottom sides. Two hexagons, placed side-by-side, form a bottom row. A third hexagon is placed on top so that it shares an edge with each of the bottom hexagons.

No colour rules
Two hexagons, placed side-by-side, form a top row. A third hexagon is placed on the bottom so that it shares an edge with each of the top hexagons.

Luis arranges his hexagon pieces in a way that resembles a tower as shown:

A description of the tower follows.

Question

Which hexagon piece must be at the very top?

  1. blue hexagon
  2. green hexagon
  3. yellow hexagon
  4. There is more than one possibility

Jumping Game

Story

Verunka has invented a game to play on her sidewalk. Her sidewalk is 13 squares long and there is a coin on the very last square.

The first square is marked START.

Verunka marks each square (except the last) with either an X or an O. Then, she begins playing by jumping on the square labelled START and using the following rules:

Verunka wins if three things happen:

  1. She can always follow the rules (i.e. remain on the sidewalk).

  2. She lands on the square with the coin.

  3. She visits all 13 squares on the sidewalk.

Question

For which marking will Verunka win the game?

  1. X, O, X, O, X, O, X, O, X, O, X, O.
  2. X, O, O, X, O, O, X, O, O, X, O, O.
  3. X, O, O, X, X, O, O, X, X, O, O, X.
  4. X, X, O, O, X, X, O, O, X, X, O, O.

Part B

Neighbours

Story

A beaver wants to visit his friend Mary. He doesn’t know which home is hers, but he has the following map of her neighbourhood, which shows homes numbered from 1 to 8, and paths between some of the homes.