Bebras "Medium" Junior Challenge Problems

Colourful tower

A little beaver girl puts rings on top of each other in this sequence:

1) Red

2) Green

3) Yellow

She repeats the sequence until the last correctly coloured ring has been placed.

How many rings will the tower have?

Answer explanation

This game is one of the simplest examples of an algorithm. In everyday life we do many kinds of actions by following sets of rules. Using rules makes doing many routine tasks easier and faster. If we can write rules exactly, describe and express them using commands, we can construct a robot to execute these commands.

Beaver hut

Programmer beaver is sorting out logs for a hut using these rules:

1st action: if log is shorter than the one to the right of it – it will be used for flooring;

2nd action: if longer, then it will be used for the roof.

Beaver is taking logs in order and repeating actions 1 and 2.

Which logs are used for the roof?

Answer explanation

In order to repeat actions in an algorithm or program, a loop is used. Loops can have a set number of repetitions (count-controlled loops) or repeat of set of commands until a condition is met (condition-controlled loops).

Read the words

Read these words by using the tree of possibilities:

Tree, trek, tram, trap, teen, teem, team.

One word is missing from the list. What is it?

Answer explanation

A binary tree is shown in the picture. A binary tree has many branches which can only have two branches attached to them. Data can be organised in this way for sorting and searching purposes.

Little stones mosaic

Robot-beaver is walking on a tile path and putting down little stones according to the commands.

When several little stones are put on the same tile they form a tower. Which program causes the robot to create a tower of 4 little stones?

• 
• 
• 
• 

Answer explanation

Understanding and reading computer programs is one of the basic computing skills. Students with some experience in programming should not have difficulty understanding a simple program using a repeat command.

Swimmer beaver

Beaver wants to swim across all rivers but he is only allowed to swim along each river once.

What is the path the Beaver needs to swim?

(type path letters with no spaces ...)

Answer explanation

This task demonstrates how graphs can be used to represent links between items. A graph is a data structure that is used a lot in computing to show relationships. Graphs also make it easier to visualize a task compared to just reading the descriptions of the relationships in text.

Missing numbers

In the picture there are numbers from 1 to 20.

Unfortunately, four numbers are missing. What are the missing numbers?

(type four numbers from smallest to largest with no spaces)

Answer explanation

When there is too much information it is beneficial to analyse the situation and identify whether this information is necessary or not. Removing unnessecary information is called abstraction. It is especially hard to analyse when we do not know how much information is missing - like in this task.

Picture of the castle

A little beaver, Lina uses an exciting method to create pictures. She cuts out a stencil of the castle in a cardboard panel. Then she places colourful bricks in it.

Lina created this picture.

In how many different ways is it possible to create this picture?

Answer explanation

This problem is solved using brute force, this method involves checking all possibilities.

Beetle robot

Beaver created a beetle robot, which can move from one square to another one following the arrows. The beetle robot starts at one of the entrances on the left.

The robot moves in the direction indicated by the arrows for as many squares as there are arrows (e.g. one square if there is one arrow, two squares if there are two arrows etc.).

When the robot is moving, he ignores the arrows on the squares.

Which starting entrances allow the robot to reach the finish?

• 1

• 2

• 3

• 4

Answer explanation

This is an example of a simple algorithm. The start and finish are given and there are rules that for the actions. Arrows in squares clearly show where to go next. These are the rules, no matter if they are explained in words or pictures. This algorithm can be carried out because the rules are clear.

A choice of tracks

Train traffic arrows control train movements at each crossing.

Which pair of instructions will result in then train arriving in London?

• 1a and 3a

• 1b and 2a

• 1a and 2b

• 1b and 3a

Answer explanation

In algorithms the outcome of a decision is either true or false, there is no in between. One of the most important programming rules – selection – can be thought of as a fork in the road. A rule determines which road to choose. In this problem the rule tells us where to go: left or right. The rules might be simple or complex.

Every other turn

Beaver created a robot cat, which moves according to the following rules:

1) Move forward

2) Turn at every other turn (every 2nd turn)

Where will cat exit?

Answer explanation

The command is a core concept in program development. The command is a clear instruction, which can be carried by a computer or robot. Commands can be written in different ways, e.g., by using words, abbreviations, symbols, arrows, but a very important thing is to strictly define the rules you use to write the commands (what each command means and what it does). In programming languages, commands are usually written using word abbreviations.