2023 Beaver Computing Challenge
(Grade 5 & 6)
Questions, Answers, Explanations, and Connections
2023 Beaver Computing Challenge
(Grade 5 & 6)
Questions, Answers, Explanations, and Connections
Five hats are hanging as shown.
In what order should the hats be rehung so that they get taller as you move left to right?
(A) \(R,P,S,T,Q\)
If we order the hats so that they get taller as you move left to right, the result is as shown below.
In computer science, arranging elements into an ordered sequence is called sorting. Sorting is one of the most fundamental problems in computer science. There are many uses of sorting: when clothes are arranged by size and colour in a store, or when the sports standings are shown in descending order. Having data in sorted order helps us make important observations about the data more quickly, such as finding the biggest value, or smallest value, or the top three values, or the middle value, etc.
There are many algorithms to sort elements. An algorithm is a process to accomplish some task. Many sorting algorithms rely on two basic principles: comparing the relative size of two values, and swapping (or exchanging the positions of) those elements. For the original order of the hats, try to think of a process to compare and swap the hats to put them into sorted order.
Lithuania
Beaver Bai has a garden with 9 fence posts around the edge, as shown.
He uses yellow ropes to divide the garden into smaller sections, according to the following rules:
Each section must be in the shape of a triangle.
One rope cannot cross another rope.
Each end of a rope must be attached to a fence post.
Which of the following gardens below could Bai have made?
(D)
In Option A, one of the sections is a quadrilateral. This breaks the rule that each section must be in the shape of a triangle.
In Option B, two of the ropes cross. This breaks the rule that one rope cannot cross another rope.
In Option C, two of the ropes attach to another rope. This breaks the rule that each end of a rope must be attached to a fence post.
Option D follows all three rules, so is the only garden that Bai could have made among these four options.
This task demonstrates the concept of triangulation: taking a polygon and decomposing it into triangles. Triangulation is a major area of computational geometry, which studies how to solve geometry problems using computer algorithms. A few of the main problems in computational geometry include computer graphics, which is concerned with generating and manipulating visual images on a computer; geographical information systems (GIS), which are systems designed to capture, store, and display data related to the surface of the Earth; and 3D modeling which represents a three-dimensional model as a two-dimensional image.
Indonesia
Karla has three maps that all show exactly the same region. One map shows the forests 
, one shows the rivers 
, and one shows the houses 
. Karla's house is in the forest, touches the bank of the river, and is House A, B, C, or D.
Which house is Karla’s house?
(A) House A
To identify Karla’s house, the information from all three maps must be considered together. This can be done by overlaying the 3 maps:
Since Karla’s house is in the forest and touches the bank of the river, it must be House A. Houses B and C are not in the forest, and House D does not touch the bank of the river.
If the information about the forests, the rivers, and the houses were shown on a single map, then it would be easy to identify the house you are looking for.
In a geographic information system (GIS), a wide variety of spatial information about the surface of the Earth is captured, stored and displayed on a computer. In particular, each different type of information, such as vegetation, buildings, water systems, or roadways is stored independently, but can be integrated in various combinations in order to more easily visualize and analyze patterns and relationships. Some applications of a GIS are emergency management when a natural disaster occurs, car navigation systems, and mapping water systems to preserve wetland habitats.
The principle of multiple layers with different image information is also used in many computer graphics programs, primarily to place visual objects in front of or behind other objects. An important question is always which layer or which objects are displayed in the foreground. In this task with three layers of images, Karla’s map of the houses should be the top layer in order for the houses to not be hidden by the forest areas.
Germany
This is a view of Andrew’s umbrella from above. The umbrella has 10 sections, each with a different design.