2024 Beaver Computing Challenge
(Grade 7 & 8)
Questions, Answers, Explanations, and Connections
2024 Beaver Computing Challenge
(Grade 7 & 8)
Questions, Answers, Explanations, and Connections
Beaver Robot can say sentences containing exactly 3 words.
Which sentence below cannot be said by Beaver Robot?
(D) YOU NEED ME
The word "ME" is the third word of the sentence in Option D but it is not in Box 3, so Beaver Robot cannot say this sentence.
Looking at the sentences in Options A, B, and C, the first words are "CAN", "BEAVERS", and "I", which are all in Box 1. The second words are "YOU", "CAN", and "LOVE", which are all in Box 2. The third words are "HELP", "SWIM", and "YOU", which are all in Box 3. Thus, the sentences in Options A, B, and C can all be said by Beaver Robot.
Creating computer programs that communicate with humans has been studied for over 60 years. In the mid-to-late 1960s, a program called ELIZA was developed to explore how simple communication between a human and computer could occur. ELIZA would ask questions, and repeat back parts of the response of the user to convey "understanding" or "listening" to the human.
Underlying these communication programs is a sentence generating system. The system used in this task is very simple. For more complex modern systems, such as ChatGPT, much more complicated systems are needed. One current popular approach used in artificial intelligence involves large language models (LLMs) which use a very large collection of data to "learn" attributes of correct sentences.
Vietnam
Ana created the following digital image.
She did her work in stages. For the last three stages, she added the following parts of the image as shown in order from left to right.
Now Ana has decided to undo some of her work, removing the parts added in the last three stages.
Which of the following options shows the resulting picture?
(D)
Undoing the last three stages of Ana’s work in reverse order results in the following sequence of pictures.
| Part Undone | Picture Before | Picture After |
|---|---|---|
| |
|
 |
| |
|
 |
| |
|
 |
The final picture above matches Option D.
This problem simulates a stack data structure that uses the LIFO (Last In First Out) rule: the item that is placed in last is the first to be removed. The objects added to the digital image by Ana can be thought of as elements put, or pushed, into a stack. When parts of the digital image are removed from the picture, these elements are removed, or popped from the stack.
Stacks are used frequently in computer science. One such usage is keeping track of operations that can be "undone", such as edits to a document, browsing history in a browser, or searching through a maze by way of backtracking if a dead end is reached.
North Macedonia
A cool new ice cream shop with a self-service machine has opened! To
place an order, you push the arrow buttons to move the robot to the
square with the flavour you want and then press 
to add a scoop to the cone. After you have chosen three scoops, your
order is prepared.
The robot always starts an order from the START square. For example, from left to right the sequence
What flavours will be on the ice cream cone, from bottom to top, if the order uses the following sequence, from left to right?
(A)
From the START square, the robot first moves to .
From , it moves to .
From , it moves to .
When an arrow button is pushed to move the robot, that is analogous to giving an instruction to a computer. A sequence of instructions is a program, which is the most common way of describing an algorithm to accomplish some goal in a language the computer understands.
When a program contains an incorrect instruction, or the sequence of instructions is not correct, this error is often referred to as a bug in the program. For example, in this task, the ice cream robot might attempt to move up when it is on the kiwi (which might have undefined behaviour) or dispense the incorrect flavour due to moving left when it should have moved right.
In order to minimize the number of bugs in a program, it is important to trace the instructions either on paper or "in your head", and also to create test cases that ensure that the program produces the expected output for particular input.
Iceland
When Pixel tries to draw lines on graph paper, she does this by colouring in blocks of tiny squares. Each of these squares intersects the line she is trying to draw. This means she cannot always draw perfectly straight lines. An example is shown where the blocks of squares Pixel coloured do not look exactly the same as the straight diagonal line that she is trying to draw.
A pattern is formed by the shapes and sizes of blocks of squares that Pixel colours. This pattern repeats every time the line she is trying to draw passes through a corner of a square. In the example, it is always 3 vertical blocks followed by 2 vertical blocks.
Pixel has started to draw the diagonal line shown and coloured in the first 8 squares as shown. If she continues drawing the line, then how will she colour the \(2 \times 3\) block of squares shown in grey?
(B)
By inspecting where this line passes through the corner of a square, we can see that the pattern for this line is 3 horizontal blocks followed by 2 horizontal blocks. Knowing this, we can extend the pattern to determine how Pixel will colour the graph paper as she tries to draw the diagonal line shown.
The \(2 \times 3\) block of squares shown in grey in the question and shown in a black box here is coloured as shown in Option B.
Creating images on a computer screen that are as realistic as possible has been one driving force in computer graphics. The limitation of resolution in the early days of computers, when the standard in the 1970s was 320 x 200 pixels, caused many graphics to seem very choppy and unrealistic. In order to help smooth out the edges of images techniques such as anti-aliasing were invented.
Notice that if the image is a horizontal or vertical line, the line will appear perfectly straight, as shown below.
In this task, one simple line drawing algorithm is demonstrated to highlight how a line which is non-vertical and non-horizontal can be approximated by a series of pixels. This algorithm uses the slope of the line to determine which pixels should be turned on or off. The underlying algorithm which was followed in this task is known as Bresenham’s algorithm. More advanced algorithms, such as the Gupta-Sproull algorithm, give a much closer approximation and more realistic image to a given line.
Canada
In a magic garden, flowers can change during the night. If there is a group of at least two flowers of the same type directly beside each other, then that group of flowers transforms into a group of different flowers as follows:
Groups of
transform to
.
Groups of
transform to 
.
Groups of transform to
.
A flower never changes more than once per night.
This is what the magic garden looks like one morning.
What will the magic garden look like after four nights have passed?
(A)
At the beginning the magic garden looks like this:
The are the only flowers of the same type directly beside each other, so
they will transform to .
Thus, after the first night, the magic garden looks like this:
Now, there are three beside each other, so they will transform to .
Thus, after the second night, the magic garden looks like this:
Now there are four beside each other, so they will transform to .
Thus, after the third night, the magic garden looks like this:
Now there are four
beside each other, so they will transform to .
Thus, after the fourth night, the magic garden looks like this:
This task illustrates three computational thinking concepts: maintaining state, sequential processing and conditional evaluation.
The representation of the flowers of the garden after each day can be thought of as the state of the system, which is updated every night. This operation of updating a state is one of the fundamental operations of the central processing unit (CPU): given the current state and some input, what new state should the computer be in?
Since there are a total of four nights passing in this task, we can think of each night as a one sequential step in the algorithm. That is, each step needs to know what the result of the previous step was, and will compute a new state from that previous step. Most computer algorithms are described as a sequential set of steps.
The transformation of the flowers can be thought of as a conditional instruction: an instruction happens only if certain conditions are met. For this task, if there is a group of flowers of the same type, then that group changes from one specified type to another. Conditional statements are often represented in programming languages using if-then-else statements, which allow certain instructions to happen only if a given decision/question has a true value.
Kosovo
In the computer game Superbebras, the background and the illusion of motion is created using a sequence of tiles.
Tiles added to the right end of the sequence are chosen according to the rules in the diagram below. Arrows point directly from each tile to the only tile(s) that can be added immediately to the right of it.
For example, a tile immediately to the right of tile 
can only be tile
or tile 
.
Which of the following images is not a possible Superbebras background?
(B)
In Option B, tile
is to the right of tile 
, but there is not an arrow pointing between them in the diagram
describing the rules (in either direction). Therefore, Option B is not a
possible Superbebras background.
Options A, C, and D are all possible Superbebras backgrounds because they do follow the rules described by the diagram.
Some computer games, such as endless runner games, have a background that scrolls horizontally, creating the illusion that the player moves through a fantasy game world. Sometimes, the background is not a constant image, but is automatically created by the computer. This automatic generation is called procedural generation: usually smaller elements are randomly combined to create a huge variety of backgrounds. However, the combination of elements cannot be completely random: the elements must obey certain rules to avoid situations the player cannot cope with.
In this task, such rules are represented by a diagram made of tiles and arrows. This diagram is an example of a directed graph, which is a collection of nodes, together with directed edges that indicate which nodes can follow each other node. Searching through a directed graph graph can be done by performing a breadth-first search (BFS), which is one way to determine which sequence of backgrounds is not possible.
The idea of searching for a path in a directed graph has many applications, such as mapping out a driving route, determining how to send information through the internet, and determining recommendations for who you may want to connect with on social media platforms.
Germany
Sequences of logs and branches are represented by codes, using the following two steps.
Let’s look at the following sequence as an example.
Continuing this process gives the sequence 3, 2, 1, 1, 1, 0. Its code is 101110.
Which of the following sequences of logs and branches is represented by the code 11101000?
(C)
In the codes, a 0 means there is an even number of branches to the right of that position in the sequence, and a 1 means there is an odd number of branches to the right of that position in the sequence. We can go through the given code digit by digit.
The first digit is a 1, which means there should be an odd number of branches to the right of the first position. The sequences in Options A and C both have 3 branches to the right of the first position, so the first digits of their codes would be 1. However the sequences in Options B and D have 4 branches to the right of the first position, so the first digits of their codes would be 0. Thus, the given code cannot represent the sequences in Options B or D. Now we can look only at the sequences in Options A and C.
The sequences in Options A and C are the same until the fifth position. The sequence in Option A has 2 branches to the right of the fifth position, so its code would have a 0 in the fifth position. The sequence in Option C has 1 branch to the right of the fifth position, so its code would have a 1 in the fifth position. The given code has a 1 in the fifth position, so it cannot represent the sequence in Option A.
If we create the code for the sequence in Option C, we obtain the sequence 3, 3, 3, 2, 1, 0, 0, 0, which has a code of 11101000, as desired.
To represent information in a computer, it must be encoded in a way that the computer can understand. In this task, the proposed encoding does not store the exact number of logs and branches, but rather a sequence of 0s and 1s that is in a more compressed representation. Even with this compressed representation, the original information (the order of the logs and branches) is able to be recovered. Therefore, for each encoding process, both the encoding algorithm and decoding algorithm need to be known.
This task is an example of a compression algorithm. Compression algorithms reduce the size of a file, such as an image or a large text document, by reducing the number of bits (binary digits) used to represent the file information, without losing information. For example, the PNG image format uses a combination of compression algorithms in order to reduce the size of the file, which reduces the time to load or store the image.
Bulgaria
Genaro uses his balance scale to weigh the spices he sells. He uses only the following 5 weights on his scale: 1 gram, 3 grams, 9 grams, 27 grams, and 81 grams.
Genaro always puts the spices on the right side of the scale. To measure 11 grams of spices, he places his weights as shown.
To help train new employees, Genaro creates codes for different amounts of spices. In his code, \(\text{L}\) means the weight is placed on the left side, \(\text{R}\) means the weight is placed on the right side, and \(\text{O}\) means the weight is placed off the scale. Genaro writes each code in order from the smallest weight to the largest weight. For example, the code for 11 grams of spices is \(\text{R}\text{L}\text{L}\text{O}\text{O}\), as shown.
| Weight (grams) | 1 | 3 | 9 | 27 | 81 |
|---|---|---|---|---|---|
| Position | \(\text{R}\) | \(\text{L}\) | \(\text{L}\) | \(\text{O}\) | \(\text{O}\) |
Among the following four codes, which measures the heaviest amount of spices?
(B) \(\text{R}\text{R}\text{R}\text{R}\text{L}\)
We look at each of the codes, to determine what they are used to measure.
For code \(\text{L}\text{O}\text{R}\text{L}\text{O}\), the total mass on the left side is \(1+27=28\)Â grams. The total mass on the right side is 9 grams. Since \(28-9=19\), the code from Option A is used to measure 19 grams.
For code \(\text{R}\text{R}\text{R}\text{R}\text{L}\), the total mass on the left side is 81 grams. The total mass on the right side is \(1+3+9+27=40\)Â grams. Since \(81-40=41\), the code from Option B is used to measure 41 grams.
For code \(\text{L}\text{R}\text{L}\text{L}\text{O}\), the total mass on the left side is \(1+9+27=37\)Â grams. The total mass on the right side is 3 grams. Since \(37-3=34\), the code from Option C is used to measure 34 grams.
For code \(\text{O}\text{L}\text{R}\text{L}\text{O}\), the total mass on the left side is \(3+27=30\)Â grams. The total mass on the right side is 9 grams. Since \(30-9=21\), the code from Option D is used to measure 21 grams.
Among these, 41 is the heaviest amount of spices, which is measured using the code from Option B.
The code created by Genaro is a variation of representing numbers in base-3, called ternary. Although base-3 is not very common in computer science, understanding how it works will help in understanding numbers in base-2, called binary numbers, which is how information is stored on a computer.
This task uses a variant of ternary numbers, called balanced ternary. Balanced ternary representation is used in applications where elements can be in one of three states: typically positive, negative, and zero/null. Some examples of these applications include electric devices, mathematical structures, and even ranking of sports teams, when the results of the game are wins (+1), draws (0) and losses (-1).
Brazil
Nine students are sitting side by side in one row in the library while their teacher conducts an online lesson from her home. The teacher sees the class from her laptop screen as shown. Each student is using a different computer, but the teacher’s screen shows who each student is sitting next to.
Which student is sitting in the middle (5th position) of the row in the library?
(D) Hannah
Based on the what can be seen on the teacher’s screen, we can determine who each student sits next to.
To begin, we can determine that James is sitting on an end of the row because only one person is right beside him:
Then, we can determine that Elke is sitting between James and Diana so she must be the student next to James:
At this point, we know the row begins with James, then Elke and then Diana. Using this approach with the rest of the views, we can determine the order of all nine students in the row:
The student sitting in the middle of the row is the one at the 5th position from left, or the 5th position from right. That person is Hannah.
The actual student arrangement in a row can be modelled as a data structure called a doubly linked list. In a doubly linked list, each node of the list contains the element value, a reference to the previous node, and a reference to the next node. In this task, each screen (node) shows the child (element of the list) and references for the child on the right and on the left of the child in the center of the screen. This task includes an exercise in traversing a list, starting from either end.
Additionally, this task focusses on visual pattern matching, which is important for computer vision. In particular, the problem of edge detection is highlighted in this task: for every student that is on the edge of a screen, we need to determine where those same features continue on the edge of another screen. These are important problems to be solved in autonomous driving: it is crucial to determine if there are pedestrians or other objects on the road, since the edge of the road and the dividing lines on the road form the edges that need to be maintained.
Malaysia
Beaver Deana enters the maze below carrying a doll of size 1. She then goes through the maze and collects dolls of different sizes, placing smaller dolls inside larger dolls.
Deana follows the arrows and obeys the following rule whenever she encounters a doll.
If the doll she encounters is bigger than the biggest doll she already has, she can choose to either take the doll and put her dolls inside of it, or leave it behind.
Otherwise, if the doll she encounters is the same size or smaller than the biggest doll she already has, she must leave the doll behind.
What is the maximum number of dolls that Deana can collect, including the size 1 doll, by the time she reaches the exit of the maze?
(C) 5
We can draw a simplified map of the maze and then an even simpler map upon noticing that all arrows move either rightwards or upwards.
All paths from the Entrance to the Exit are 6 steps long so the maximum number of dolls Deana can carry is 6. By the rule and because the biggest doll is of size 6, if she collects 6 dolls, they must be of sizes 1, 2, 3, 4, 5, and 6, and picked up in that sequence.
Notice that the only one way to pick up a doll of size 3 and also a doll of size 4 is to begin by moving right to pick up the doll of size 3, then moving either right again or up and choosing to leave the doll of size 5 behind, and then choosing to pick up the doll of size 4. In this case, Deana cannot pick up and carry a doll of size 2. This means the answer is at most 5.
Here are two ways Deana can carry five dolls out of the maze. The dolls she takes are indicated in grey.
This task asks us to find the longest increasing sequence of doll sizes across all paths from the entry to the exit. For a single path, the longest increasing subsequence problem is a standard algorithmic problem. The problem statement is that given a list of numbers, pick numbers that form the longest sequence that is constantly increasing. For example, the sequence 4, 10, 3, 3, 20 would have the subsequence 4, 10, 20 as the longest increasing subsequence. There is an efficient algorithm that uses dynamic programming to remember partial solutions of shorter subsequences without having to recompute them.
Searching for the longest such sequence across multiple paths in a two-dimensional grid is a more complex problem. In the maze in this task, the paths have a simple structure (all of equal length, going only up and right) and our simple analysis was sufficient to find the answer.
For more complicated mazes, a more general approach is needed to systematically explore all possible paths. If the maze is small enough, the process of backtracking can be used to examine all possible paths. However, when playing a game like chess or Go, where there are a huge number of possible moves, it is not feasible to explore all paths. So we try to identify moves that will not be useful in reaching a good outcome and we stop exploring such paths as we go along, using various heuristics.
Taiwan
Manas creates drawings by combining some of the following images:
| Image |  |
 |
 |
 |
 |
 |
 |
 |
|---|---|---|---|---|---|---|---|---|
| Name | cloud | crown | flower | person | pizza | star | sun | smiley sun |
Manas draws on cards following one, single, secret rule. He has created four cards that obey this rule:
Anil observes the cards and creates a new card, but it does not obey the rule.
Which of the following could be the secret rule?
(C) If there is a person holding pizza on the card, then there is no crown on the card.
Option A is incorrect because there is a cloud on Manas’ second (and third) card but also flowers on Manas’ second (and third) card.
Option B is incorrect because Anil’s card has a person holding pizza on it which means it does obey the secret rule.
Option D is incorrect because Manas’ fourth card has neither a smiley sun nor a cloud on it.
Option C is correct because all four of Manas’ cards obey this rule and Anil’s card does not. Specifically, Manas’ first and fourth cards have a person holding pizza and not a crown, and their second and third cards do not have a person holding pizza. Anil’s card has a person holding a pizza on it, but also a crown.
This task involves logical reasoning. Specifically, the key component of the task is reasoning about the cards and the possible rules that involve logical OR expressions, logical NOT expressions, as well as conditional logical inference.
Some of the possible secret rules involve the logical connective OR. For example, rule (B) states that there must be a star on the card OR there is a person holding a pizza on the card. In order for an OR expression to be true, at least one of the two component expressions must be true.
Other rules, such as rule (A), state that in some case, there must NOT be any flowers on the card. In order for the NOT (or negation) of an expression to be true, that expression must be false.
Finally, conditional logical inference appears, for example, in rule (C), which states that IF there is a person holding pizza on the card, THEN there is no crown on the card. Conditional logical inference is used frequently in many programming languages which contain if-then-else statements.
Logic plays a key role in computer science in a huge variety of areas: databases, programming languages, artificial intelligence, hardware and software design and verification, etc. Logic is one of the fundamental concepts that underlies computational thinking: being able to take information, model it logically, and make logical conclusions from that model.
India
Bernard has wrapped gifts for the 14 students in his class, and numbered the gifts from 1 to 14.
Bernard knows the weight of each gift. After wrapping each gift, Bernard realized that he accidentally dropped his phone in one of the boxes. In order to avoid unwrapping many gifts, he plans to do the following:
In which of the following situations would Bernard weigh the fewest number of piles?
(C) The phone is in gift number 8.
We look at all the possibilities for the retained piles. These are illustrated in the following diagram, where each pile is indicated by a box.
Notice that if gifts 1 or 8 contained the phone, it could be found after weighing exactly three piles. In all other cases we must weigh four piles. Thus, of the options given, the situation that requires the fewest number of piles to be weighed is if the phone is in gift number 8.
This task highlights a problem solving technique called divide and conquer. In computer science, a divide and conquer approach to solving a problem is to repeatedly divide a problem into several non-overlapping subproblems, solve the subproblems, and combine the subproblem solutions.
In this task, notice that every time the problem is divided, we can remove one of the subproblems: that is, approximately one half of the remaining boxes are no longer under consideration. This approach to solving this task is a variant of binary search, which searches for a value in a sorted list of values and is exponentially faster than searching linearly through that list of values.
Romania
A group of beavers left their house 
.
Some of them went to the museum 
, and the rest of them went to the forest 
.
Beavers documented their various travels in the map below. Each circle is a place where beavers could pass through, and the lines between them are the paths they could take. Each path is labelled with an arrow indicating the direction the beavers took on that path, and also a number indicating the number of beavers that took that path. For example, three beavers took the path to the museum.
Unfortunately, some documentation is missing, so some paths are missing their label.
How many beavers went to the forest?
(A) 16
We begin by labelling the intersections as shown below. The beavers that went to the forest must have gone through F or E. The only way to F is from C or D. We know that 4 beavers arrived from C, but we do not know how many arrived from D. Therefore, we consider the paths connected to D. From the house, there are 9 beavers that went to D. This means there are also nine beavers that left D. This can happen either on the path to C (2 beavers), to E (6 beavers) or to F. Therefore, only 1 beaver went from D to F path because \(9 - (2 + 6) = 1\). This is what we know now:
Next, we consider the path from F to the forest. There are \(4 + 1=5\) beavers that went to F: 4 from C and 1 from D. Since 3 beavers went to the museum from F, this means that 2 beavers went to the forest because \(5 - 3 = 2\). We can use this to update what we know at this point:
We still need to find out how many beavers went to the forest from E. There are 6 beavers that went from D to E. And, because 8 beavers went to B from the house and there is only one path leaving B, 8 beavers also went from B to E. In total, \(6 + 8 = 14\) beavers went to E. There is also only one path out of E so all 14 of these beavers went from E to the forest. We now have all the information we need:
Summing up the numbers of beavers that went from F to the forest and from E to the forest, we determine that \(2 + 14 = 16\) beavers went into to the forest.
This task involves a concept from graph theory called a weighted directed graph.
A directed graph is a collection of nodes (or vertices) connected by directed edges. For example, if \(u\) and \(v\) are two different places on a map, a directed edge may go from \(u\) to \(v\) to indicate that it is possible to travel from \(u\) to \(v\). In a weighted graph, each edge has a numerical weight attached to it. This weight can represent a variety of quantities: the length of a road, the maximum capacity of a river system, the toll cost for a highway, or the frequency of traversal along that path. In this task, the numbers on the directed edges indicate how many times a beaver has travelled along that path.
Additionally, this task utilizes the concepts of in-degree and out-degree of a vertex. The in-degree refers to the sum of weights of inbound edges to a node, while out-degree refers to the sum of weights of outbound edges from a node.
There are many applications of weighted directed graphs: determining the least expensive flight path between two cities, the quickest path in the internet to send an email message, or how to transport electricity through an electrical grid with the least amount of wasted energy.
Slovakia
Quinn and Evan are playing a game on the beach involving shells, holes, and lines in the sand.
To play the game, they take turns placing new shells in empty holes, some of which are connected by lines. The first person to have two of their shells placed in holes directly connected by a line loses the game.
Quinn plays with one type of shell: 
, and Evan plays with another type of shell: 
.
The game has started and each player has completed two turns. The placement of these four shells are as shown, and the remaining empty holes are numbered 1 through 7.
It’s now Quinn’s turn. In which empty hole should Quinn place her shell if she wants to guarantee a win in the game?
(D) 7
Quinn will lose immediately if she places a shell in holes 1, 3, 4, or 6. This means she is left to choose hole 2, 5, or 7 if she wants a chance to win.
If Quinn places her next shell in hole 2, then Evan might place a shell in hole 7. At that point, Quinn must place a shell in hole 5 to avoid losing immediately. Evan can follow by placing a shell in hole 3, and Quinn will immediately lose on her next turn.
Similarly, if Quinn places her next shell in hole 5, then Evan might place a shell in hole 7. At that point, Quinn must place a shell in hole 2 to avoid losing immediately. Evan can follow by placing a shell in hole 3 and Quinn will immediately lose on her next turn.
Instead, suppose Quinn places a shell in hole 7. Then Evan must place a shell in hole 1, 2, 3, 4, 5, or 6. He will lose immediately if he places a shell in 1, 4, 5, or 6. If he places a hole in 2 or 3, then Quinn can place a shell in hole 5. At that point, Evan will immediately lose when he places his next shell. Therefore Quinn is guaranteed a way to win the game by placing a shell in hole 7.
Games such as this are studied by game theorists. In particular, the discovery and implementation of winning strategies such as the one we discovered for Quinn is a key concept of algorithmic game theory.
Game theory has applications to economics, biology, and computer science. Specifically, current problems in computer science are being solved using game theory. These problems can arise anytime there is some sort of "competition". In economics this could be competing companies. In biology, different species of plants compete for sunlight and different species of animals compete for food.
More technically, in the field of artificial intelligence, systems often consist of agents that behave like players in a game. Classical algorithms such as minimax and negamax can be used to find winning strategies and more modern machine learning algorithms can solve more complex problems involving large quantities of data using game-theory techniques.
Another application of game theory arises in network security. The interaction between an attacker and the network administrator can be modelled as an attack-and-defense game.
Canada
Fleas A, B, C, and D start a race, in that order, from position 1 in the picture shown.
They continue to take turns in this order (A, B, C, D, A, B, \(\ldots\)) and follow two rules:
It is possible for more than one flea to be at the same position at the same time.
Which flea will finish first?
(C) \(C\)
A scheme for the route of each flea is shown from which we can see that flea C finishes first. Yellow circles represent the positions of individual fleas A, B, C, and D after the 15th turn (when flea C reaches the final position). Yellow lines show their routes. The jumping arrows are numbered as J1 to J6 followed by A, B, C, or D indicating the flea using the arrow, after which the arrow disappears. A solid arrow indicates an arrow available for use. A dashed arrow means that it has disappeared.
A few observations can make it more clear why \(C\) is the winner:
Computers can simulate many phenomena and processes. For example, a competitive struggle between various opponents, where one player may gain a short-term advantage or, conversely, a short-term disadvantage, depending which decisions were made. If the phenomena can be modelled and changes modelled with an algorithm, a computer will be able to predict and simulate the result.
This task is an example of a dynamic system, where the state of the system changes when flea reaches a position with a green arrow. This operation of updating a state is one of the fundamental operations of the central processing unit (CPU): given the current state and some input, what new state should the computer be in?
A very well-known case of evolution simulation is the fox-rabbit population problem. It predicts the development of the rabbit and fox population on an isolated island. Foxes eat rabbits, and when they eat a lot of them, they run out of food, starve, and die too. Fewer foxes will then allow rabbits to multiply faster.
A computer can be a very helpful tool to model, analyze, and predict outcomes based on changes to the system. The fox-rabbit population problem can be visualized using the following website:
Many dynamic systems, such as weather systems or stock markets, can be modelled and analyzed using computer models.
Czechia
