Bebras "Difficult" Junior Challenge Problems

Beautiful tiles

Robot-beaver is walking on tiles and decorating them with ornaments. He knows these commands:

Several flowers on the same tile are drawn next to each other.

What is the largest number of flowers drawn on a single tile by robot-beaver, after these commands?

(type a number only ...)

Answer explanation

This problem introduces programming. The presented set of commands is a very simple programming language. The programming language for different actions has functions (move, draw) with arguments and a loop.

Beaver map

On the beaver map the location of objects are indicated by two numbers in brackets. Row number first, then – column number.

Lake (1, 1)

Bridge (5, 6)

The beaver hut is located four points below bridge and two points to the right of the bridge.

What is the location of the Beaver hut?

(type two numbers with no space)

Clothes line

Kangaroo built a clothes dryer. They want to strengthen the poles to save the dryer from beavers. Unfortunately, they can only afford to strengthen one pole.

In which pole should they invest?

(click on the correct pole ...)

Answer explanation

Graphs are useful to model all kinds of real life problems, like traffic, maps and phone connections. In computing algorithms are often used to work with graphs.

Swap

Beaver’s and kangaroos’ cards are in an order.

You can swap two cards next to each other.

How many swaps are needed to swap cards to get all beavers at the beginning of the row and kangaroos at the end? Use the minimum number of swaps.

(type a number only ...)

Answer explanation

Typically, automatic processing of data is much easier, when data is arranged according to some criteria – then it is sorted. The method for sorting the set of cards that is described in this task is called “bubble sort”. This sorting algorithm steps through a list of objects again and again, swapping any neighbouring objects which are in the wrong order. The list is sorted when no swap occurs during a pass through the list. Bubble sort is quite easy to understand compared to other sorting algorithms. But unfortunately, it is not very efficient.

iFrog

Robot frog can grab one insect by jumping once from one leaf to another one.

How many jumps does robot frog have to make in order to to grab all the insects?

(type a number only ...)

Answer explanation

This task shows the concept of optimization. Optimization can be defined as finding the most efficient solution. Therefore, here a strategy is needed to find the best solution among all feasible solutions.

Laundry

Beaver has a laundry with two separate machines for washing and drying. Both machines have an half hour operating cycle, so each customer needs 60 minutes.

Two beavers arrive in a hurry. They need to wash and dry their clothes as quickly as possible.

How many minutes it is going to take to wash and dry clothes for two beavers?

(type a number only ...)

Answer explanation

This task deals with parallel processing, where tasks which do not conflict can be run simultaneously. Most of today‘s CPUs are multi-core machines, which can perform parallel processing. Parallel processing is an important technique, which can be applied to factories producing cars and many other areas.

Robot is carrying

Robot-beaver is programmed to carry parcels to the third floor. If a parcel weighs up to 10 kilo, robot can move one floor per minute. If it is heavier 2 minutes per floor. Robot-beaver delays 1 minute preparing to move before each flight of stairs.

How many minutes will it take Robot-beaver to carry a 13 kilo parcel to the 3rd floor?

(type a number only ...)

Answer explanation

A condition IF – THEN – ELSE is one of the most important commands in algorithms. A condition determines which action should be taken. If the result of the condition is true, the action, which is described after “then”, is taken. If the result of the condition is false, the action which follows “else” is taken. These situations are also common in the real world when we have to make a choice between two options.

Read around

A wheel is programmed to stop according to the following rules:

1st time – skip one square,

2nd time – skip two squares,

3rd time – skip three squares etc.

The first letter of the word is “P”.

What is the word?

Answer explanation

The rules of the game are an example of an algorithm, which is applied in order to create a word. In everyday life we follow certain rules to be able to perform tasks. Actually these rules represent a certain type of algorithm. When everything is clear and defined by rules, a computer program can be developed to perform the algorithm.

Necklace for a little beaver

Little beaver wants to give a necklace to his girlfriend beaver. He knows she wants a specific one:

1) Red berries have to be between pine needles and

2) The number of apple pips has to be equal to the number of pine needles.

Which necklace will little beaver girl like?

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Answer explanation

In computing it is important to be able to spot patterns which may be useful to us. Pattern matching helps us find similarities in things that may look different at first, but have something in common. When we detect that a new problem is similar to another problem we have already solved, we can apply a similar solution.

Programmer’s New Years Eve

Programmer beaver decorated an extraordinary Christmas Tree especially for a New Year’s Eve. A lit light bulb means 1 and unlit means 0.

Which New Year Eve is being celebrated?

(type four numbers for the year ...)

Answer explanation

The binary number system plays a central role in how information of all kinds is stored on computers. Understanding binary can lift a lot of the mystery from computers, because at a fundamental level they’re really just machines for flipping binary digits on and off. Binary representation is used extensively in computing, since all data are stored as bits, and each bit can take either 0 or 1 as a value.