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Task examples

The ability of students to solve tasks is important for the development of their various skills. Students should be able to understand the information given, identify the critical features and their interrelationships, construct or apply an external representation, finally, take right decision for solving the task. Interest in contest essentially depends on tasks. Attraction, invention, tricks, surprise should be desirable features of each task presented to contest. The tasks have to be selected carefully, taking into account the different aspects of each task, i.e. what educational power it contains and how to interpret its’ attractiveness to students.
Click on presented icons and look at the tasks that you can get during the Bebras challenge.

Benjamins Task Examples

Ages 11-12

       

Dress code for beavers

(Age group: Benjamins; Difficulty: easy; Category: ALG, STRUC)

Beavers like complex rule systems and have therefore established a new dress code. Some beavers don’t use the correct combination of clothes. Use the graph to determine which beaver is dressed correctly. The graphic is called a tree because there is a single root node (the topmost) with branches connecting other nodes – like a real tree. At every node you have to decide which direction you want to go within the tree, you can’t go up again.

Which beaver is not dressed like the dress code?

Answer:

    B      C      D     

Solution:

The second beaver (answer B) is dressed not by the dress code. He should have a blue hat instead of a red one.

It's Informatics

This is an example of a decision tree used in pattern recognition. A decision tree is a graph that uses a branching method to illustrate every possible outcome of a decision.

 

Water supply

(Age group: Benjamins; Difficulty: medium; Category: STRUC)

Beaver has constructed a pipeline system to water his apple tree.

The expressions contain variables A, B, C, D, which may be true or false. A variable has the value true, if the corresponding gate is open, and false, if it is closed.

In which case the apple tree gets water?


Answer:

A: A = false, B = true, C = false, D = false
B: A = true, B = true, C = false, D = false
C: A = true, B = false, C = false, D = true
D: A = false, B = false, C = false, D = true

Solution:

Correct answer is A. Since B is open and A is closed, water comes to tree.
B: Since A is open, the water coming from B goes directly down through A.
C: Since B is closed, there is no water coming from the left source. Since C is closed, the right source is also blocked.
D: Since B is closed, there is no water coming from the left source. Since C is closed, the right source is also blocked.

It's Informatics

Computer programs process data structures that model real things. A model is an abstraction, a simplified image of some real scenario. In this case the gates are represented by variables that contain the values open or closed. This is an abstraction, since all other properties of gates are ignored.

Cadets Task Examples

Ages 13-14

   

Cloud of Castoria

(Age group: Cadets; Difficulty: medium; Category: INF, USE)

The Castorians store their data in a cloud of four interconnected server computers. The picture shows all the connections between the servers.
For a higher data safety all data is stored on both store servers STORE-1 and STORE-2.
For a higher access probability all data is accessible through both port servers PORT-1 and PORT-2.
The data is stored only on store servers and port servers do not store any data.
STORE-1 is accessible through STORE-2 and vice versa.

Which statement is FALSE ?


Answer:

A) If STORE-1 and PORT-2 are destroyed then all Castorian data is inaccessible.
B) If STORE-2 and STORE-1 are destroyed then all data in the Castorian cloud is lost.
C) If PORT-1 and PORT-2 are destroyed then all Castorian data is inaccessible.
D) If PORT-2 and PORT-1 are destroyed then all data in the Castorian cloud is lost.

Solution:

The answer D is false. If PORT-2 and PORT-1 are destroyed then all data in the Castorian cloud is inaccessible, but not lost.

It's Informatics

For any data there are risks to become inaccessible for some time, or to get lost definitively. If you manage the storage of your data yourself, you decide yourself, what risks you take.
If you transfer the responsibility for your data to an Informatics service company, you should know what risks they take. Besides loss and inaccessibility there are many more risks. E.g. your data might be copied and misused by someone, so your privacy is hurt. Your data might be changed maliciously, so you cannot trust it anymore.
Is the careless "cloud" metaphor just a commercial trick to obscure from you the many risks you take when giving away the responsibility for your data?

 

Fast laundry

(Age group: Cadets; Difficulty: easy; Category: ALG)

Beaver Joe has started a new laundry business. He has got three machines: a washer, a dryer and a pressing iron. Every machine is connected through its own timer which provides for half an hour of electricity.

So, when a client arrives, he needs 90 minutes for all of the three procedures. And three clients using the machinery consequently need 270 minutes.

But now, there are three beavers arriving which are really busy. Each one them has enough clothes for a load of its own. But they agree that they want to finish as quickly as possible.
How many minutes does it take for all three of them to finish their laundry?

Answer:

A) 90 minutes B) 120 minutes C) 150 minutes D) 270 minutes

Solution:

Answer C) is correct: beaver 1 needs 90 minutes anyway. During his use of the dryer, beaver 2 starts with washing, and finishes drying at the same time that beaver 1 is finishing with the iron and beaver 3 finishes his washing. So beaver 3 needs two more turns (dryer and iron). This is a total of the 90 minutes for beaver 1 plus the two turns of beaver 3 (60 minutes), which is 150 minutes.

It's Informatics

CPUs are working in a similar way as the laundry. If every device is used as soon it is free, computation becomes faster. Pipelining is an important idea for constructing CPUs. It’s a cheap way to speed up computation.

Juniors Task Examples

Ages 15-16

       

Friends

(Age group: Juniors; Difficulty: medium; Category: STRUC, SOC)

Lucia and her friends are registered in a social network. Here are Lucia's friends and their friends.

A line means friendship between two people. For example Monica is Lucia's friend but Alex is not Lucia's friend.

• If someone shares a photo with some of his/her friends then those friends can also comment on it.
• If someone comments a photo then all his/her friends can see the comment and the photo, but cannot comment on it unless they originally could.

Lucia has uploaded a photo. With whom can she share it if she does not want Jacob to see it?

Answer:

A) Dana, Michael, Eve
B) Dana, Eve, Monica
C) Michael, Eve, Jacob
D) Micheal, Peter, Monica

Solution:

A) is correct. Lucia has 6 friends. Dana, Michael and Eve aren’t friends with Jacob, so they can’t see Lucia’s photo by the rule, that if someone comments a photo then all his/her friends can see the comment and the photo.

It's Informatics

Managing access to private information is very important nowadays. When uploading private pictures to the Internet, one always has to think carefully about who might see the picture, even in the future. Many employers today check for additional information about an applicant. Since it is very difficult to actually control who can see a picture, best is never to upload pictures to the Internet except pictures, you would also put on public display at your local bus station or school.

The structure displayed in the picture represents a graph. Graphs are an important tool in informatics to represent things like social networks. A simple graph consists only of nodes (representing persons in a social network) and edges (representing friendship relations). Methods to automatically analyze graphs are very useful, not only for social networks but also for example in a GPS application, where crossroads are represented by nodes and the streets between correspond to edges. Then a computer program can use this graph to find the shortest way between two places.

Password machine

(Age group: Juniors; Difficulty: medium; Category: INF)

In the school’s computer lab the beavers have to set new passwords for their accounts. They are allowed to use lower-case letters, capital letters and the digits from 0 to 9. Each password must have a typical order to be accepted.

A-Z means any capital letter from the alphabet.
0-9 means any digit.
a-z means any lower-case letter from the alphabet.
There are certain rules for the password to be accepted.


In a loop any quantity of letters or digits can be used several times. In this loop the beavers are allowed to use zero, one or more capital letters.


An edge means that the beavers have to use exactly one letter or digit. This edge demands one lower-case letter.


Which of the following passwords won’t be accepted?

Answer:

A) 123aNNa
B) Peter3ABCd
C) 2010Beaver4EVEr
D) bENNOZzz

Solution:

D) “bENNOZzz” is the password that won’t be accepted. It ends with a capital-case letter followed by two lower-case letters, which isn’t allowed.
A) “123aNNa” , B) “Peter33ABCd” and C) “2010Beaver4EVEr” are legitimate.

It's Informatics

The graphic of an abstract machine, a theoretical model of a computer hardware or software system, is a good way to visualize and understand how computers, programs, etc. deal with input. It also shows the visualization of rules.

 

Seniors Task Examples

Ages 17-18

       

Paper Folding

(Age group: Seniors; Difficulty: medium; Category: ALG, INF)

The Beaver has developed a programming language for paper folding. This language can be used to explain how to fold any piece of paper with straight sides. One of the commands in this language is fold.
e = fold(a, b) means:
fold the piece of paper in a way that side a is lying completely on side b.
In that way you create a new side, the fold. This line is called e.
Example:

Please note, that the paper remains on the table during folding, and that the length of side b is twice the length of side a.

How does the paper rectangle (a, b, c, d) look like after the execution of these three commands?

e = fold(c, a); f = fold(c, d); g = fold(a, f)

Answer:

    B      C      D     

Solution:

The correct answer is A. The following images explain the execution of the fold-operation step by step.

It's Informatics

Functions are an important concept in programming. A function call is considered to be the start of some activity. Programmers say: The function accepts some parameters (here: two sides), processes some data and returns an object (here: the fold). This is different from the concept of functions in mathematics.

Plant Life

(Age group: Seniors; Difficulty: easy; Category: ALG)

The Beaver loves flowers. May be this is the reason why he has invented a simple programming language for visual design based on the idea of plant life.
Each picture starts with a square called a. A visual object can perform three operations: grow(), split() and die().
The following program explains the semantics:

                                                    a.grow(east); a.grow(east) ;


b,c = a.split(); c.grow(north); b.die();

Please note, that only an oblong object may execute the split()-Operation producing two shorter Objects of equal size. A square cannot be split.
Beaver wants to write a program that transforms the left image to the right image. Which could be the first four commands of this program?


 

Answer:

A. a.grow(east); a.grow(east); b,c = a.split(); b.die();
B. a.grow(north); a.grow(east); a.grow(east); b,c =a.split();
C. a.grow(east); a.grow(east); a.grow (north); a.die();
D. a.grow(east); b,c = a.split(); c.grow(north); c.grow(east);

Solution:

The correct solution is A. This is the complete program: A. a.grow(east); a.grow(east); b,c = a.split(); d,e = c.split(); b.die(); d.die(); e.grow(north);

C does not work because after the fourth command the image is empty. B and D result to rectangles with minimum side lengths of two units. It is impossible to reduce such a shape to a rectangle with a minimum side length of one unit using the split()-Operation. A gardener must grow things carefully!

It's Informatics

Computer programs, class libraries and programming languages are often based on intuitive metaphors. This makes is easier for a human programmer to understand and use them. For example the LOGO graphics system uses the idea of a moving turtle pulling a pen over the ground. In this task the Beaver adopted the idea of vegetation. Plants cannot walk from one spot to another, since they do not have legs and muscles. But plants can grow, reproduce vegetative and die. With these operations they can implement locomotion in a special way. This is an algorithmic facet of biology.