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About
Sum Number Game
Translations
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Credits
Shaun Quek; Loo Kang Wee; based on idea by Theresa Heng
1. Core Game Mechanics and Objectives:
The fundamental gameplay involves two players taking turns removing single numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} until only three numbers remain. The objective of the game differs for each player:
- Player 1's Objective: Wins if the sum of the final three remaining numbers is not a multiple of 3.
- Player 2's Objective: Wins if the sum of the final three remaining numbers is a multiple of 3. The game description explicitly states, "If it is a multiple of 3, that is a trinket, then Player 2 wins the game; otherwise, player 1 wins."
The game is sequential, with Player 1 making the first move: "First, Player 1 will pick a number from the board. Then Player 2 will continue to pick a number from the rest of the numbers on the board. This game will continue until there are 3 numbers left on the board..."
2. Educational Value and Target Audience:
The game is explicitly intended to enhance understanding of basic mathematical operators: "The objective of this game is to help students gain a better understanding of basic mathematical operators." The inclusion of the game under the "Mathematics" category and alongside topics like "whole numbers," "Addition and Substraction," and "Multiplication and Division" within the "Open Educational Resources / Open Source Physics @ Singapore" platform highlights its pedagogical aim.
3. Strategic Elements:
Despite its simple rules, the game possesses strategic depth. The description from the "King Trikan" excerpt elaborates on the potential strategies employed by the players:
- Blocker Strategy (Implicit for Player 1): Player 1 can adopt a strategy of selecting numbers that would prevent the remaining three numbers from summing to a multiple of 3. The excerpt states, "A player deploying the Blocker strategy aims to thwart their opponent's chances of achieving a multiple of 3. By meticulously selecting numbers, the Blocker strategy seeks to obstruct the path to victory..."
- Strategist Approach (Implicit for Player 2): Player 2 can focus on identifying and removing numbers that leave a potential combination of three whose sum is a multiple of 3. The excerpt explains, "Embracing the role of the strategist, a player assesses the ever-evolving board, evaluates potential moves, and anticipates future scenarios. This approach aims to ensure a winning position by making informed, calculated decisions."
The description emphasizes the "interplay between two human minds" and how "each decision into a pivotal moment," highlighting the cognitive engagement the game fosters.
4. Platform and Accessibility:
The game is implemented as a JavaScript HTML5 Applet, making it readily accessible through web browsers without the need for additional software. The "King Trikan" excerpt provides an embed code, suggesting ease of integration into webpages:
<iframe width="100%" height="100%" src="https://iwant2study.org/lookangejss/math/ejss_model_sum_numberCardGame/sum_numberCardGame_Simulation.xhtml " frameborder="0"></iframe>
The availability of the game under the "Open Educational Resources / Open Source Physics @ Singapore" initiative indicates a commitment to free and accessible educational tools.
5. Context and Collaboration:
The credits section of both sources indicates that the game is based on an idea by Theresa Heng and developed by Shaun Quek and Loo Kang Wee. This highlights a collaborative effort in creating this educational resource. The mention of "Compiled with EJS 6.1 BETA (201115)" suggests the use of the Easy JavaScript Simulations Toolkit in its development.
6. "King Trikan" Title Connection:
The "King Trikan" title associated with the game in one of the excerpts is not explicitly explained in the provided text. However, its inclusion suggests it might be an alternative name or a project name under which this specific game variation was developed or hosted.
7. Variations and Further Exploration:
The "King Trikan" excerpt mentions a version of the game played with odd numbers (1, 7, 9, 11, 13, 15, and so on) in its introductory text, although the detailed rules provided later revert to the 1-9 set. This hints at potential variations of the core game mechanics that could be explored for different learning objectives or increased complexity.
Conclusion:
The "2 Players Sum and Subtract Number Card Game" is a simple yet strategically engaging game designed to reinforce basic mathematical skills, particularly addition and divisibility by three. Its accessibility as a web-based applet and its open educational resource status make it a valuable tool for educators looking for interactive ways to teach fundamental mathematical concepts. The game encourages strategic thinking and highlights the interplay between players' choices in achieving their respective winning conditions. Further investigation into the "King Trikan" context and the potential variations of the game could provide additional insights into its educational applications.
Strategic Number Card Game Study Guide
Key Concepts
- Game Objective: Player 2 wins if the sum of the final three remaining numbers is a multiple of 3; otherwise, Player 1 wins.
- Gameplay: Two players alternate turns removing one number at a time from a starting set of numbers (1-9 in one version, a set of odd numbers in another described version). The game ends when only three numbers remain.
- Winning Condition (Player 2): The sum of the final three numbers is divisible by 3 (remainder is 0 when divided by 3).
- Winning Condition (Player 1): The sum of the final three numbers is not divisible by 3 (remainder is 1 or 2 when divided by 3).
- Number Sets: The game can be played with the numbers 1 through 9, or a set of odd numbers. The outcome and strategies may differ based on the number set.
- Strategic Thinking: Players must think ahead and consider the numbers remaining and how their choices will impact the final sum.
- Blocker Strategy: A strategy focused on preventing the opponent from achieving a sum that is a multiple of 3.
- Strategist Approach: A strategy focused on analyzing the board and making calculated decisions to achieve a winning outcome.
- Multiples of Three: Numbers that can be divided by 3 without a remainder (e.g., 3, 6, 9, 12, etc.). Understanding which combinations of numbers sum to a multiple of three is crucial.
Quiz
- Describe the initial setup of the 2-player number card game as presented in the sources.
- What is the specific condition that determines a win for Player 2 in this game?
- How does Player 1 achieve victory in the 2-player number card game?
- According to the provided text, what are the two main strategic approaches a player might employ during the game? Briefly explain each.
- What happens when there are exactly three numbers left on the board, and how is the winner determined at this stage?
- In the "King Trikan" version, what is the initial set of numbers from which players remove cards?
- Explain the concept of a "trinket" in the context of this card game.
- How does the game abstractly implement strategic thinking, according to the "Strategic Duel" text?
- Who are credited as the individuals behind the idea and compilation of this game?
- What is the core mathematical concept that the game aims to help students understand better?
Quiz Answer Key
- The game starts with a set of numbers on a central board. In one version, this set is the numbers 1 through 9. Two players then take turns removing one number at a time from this set.
- Player 2 wins if, after all but three numbers have been removed, the sum of these three remaining numbers is a multiple of 3 (i.e., divisible by 3 with no remainder).
- Player 1 wins if, at the end of the game when only three numbers remain, their sum is not a multiple of 3. This means the sum will have a remainder of 1 or 2 when divided by 3.
- The two main strategies are the Blocker strategy, where a player tries to prevent their opponent from achieving a sum that is a multiple of 3, and the Strategist Approach, where a player analyzes the board and anticipates future scenarios to make winning decisions.
- When only three numbers remain, their sum is calculated. If this sum is a multiple of 3, Player 2 wins. If the sum is not a multiple of 3, Player 1 wins.
- In the "King Trikan" version of the game, the initial set of numbers from which players remove cards is the set of whole numbers from 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8, 9).
- In this card game, a "trinket" represents the winning condition for Player 2. It is achieved when the sum of the final three remaining numbers is a multiple of 3.
- The "Strategic Duel" text explains that the game implements strategic thinking through the human decision-making processes of the players, rather than lines of code. Their mental calculations and analyses drive the gameplay.
- Shaun Quek, Loo Kang Wee, and Theresa Heng are credited. The game is based on an idea by Theresa Heng and compiled by Shaun Quek and Loo Kang Wee.
- The objective of the game is to help students gain a better understanding of basic mathematical operators, particularly addition and the concept of multiples.
Essay Format Questions
- Analyze the strategic considerations for Player 1 and Player 2 in the 2-player number card game. How might their goals and approaches differ throughout the game?
- Discuss how the specific set of starting numbers (e.g., 1-9 versus a set of odd numbers) could influence the gameplay and the strategies employed by the players. Provide potential examples.
- Evaluate the effectiveness of this card game as a tool for learning basic mathematical concepts. What specific mathematical skills does it reinforce, and why might this game be engaging for students?
- Compare and contrast the "Blocker Strategy" and the "Strategist Approach" in the context of this game. Under what circumstances might one strategy be more effective than the other?
- Considering the game mechanics and winning conditions, explore the mathematical properties of numbers that make certain strategic moves more advantageous than others in this 2-player card game.
Glossary of Key Terms
- Multiple of 3: An integer that can be divided by 3 without leaving a remainder (e.g., 3, 6, 9, 12).
- Remainder: The amount left over after one integer is divided by another. In this game, the remainder when the sum of the final three cards is divided by 3 determines the winner.
- Strategy: A plan of action designed to achieve a long-term or overall aim. In this game, players employ strategies to try and manipulate the final three numbers.
- Tactics: Actions or maneuvers taken to gain a short-term advantage in a game, often in service of a broader strategy.
- Game State: The current situation in the game at any point in time, including which numbers have been removed and which remain.
- Turn-Based: A game where players take turns to perform actions.
- Set (of Numbers): A collection of distinct numbers used at the start of the game.
- Sum: The total obtained by adding two or more numbers. The sum of the final three numbers is crucial for determining the winner.
- Winning Condition: The specific criteria that must be met for a player to win the game.
- Open Educational Resources (OER): Teaching, learning, and research materials that are freely available for everyone to use, adapt, and share.
Sample Learning Goals
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For Teachers
2 Players, Sum Number Game Javascript HTML5 Applet
- 2 Players take turns to remove one number at a time from the set of numbers 1, 2, 3, ..., 8, 9 from the board in the center.
- First, Player 1 will pick a number from the board
- Then Player 2 will continue to pick a number from the rest of the numbers on the board.
- The gas will continue until there are 3 numbers left on the board. The sum of these 3 numbers will be calculated. If it is a multiple of 3, that is a trinket, then Player 2 wins the game; Otherwise, Player 1 wins.
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| Game state after player 1 wins |
**Title: The Strategic Duel: Unraveling the Intricacies of the 2-Player Card Game**
*Introduction*
Within the realm of strategic games, a hidden gem beckons those who seek a cerebral challenge. Enter the enigmatic world of a 2-player card game that intricately weaves intellect and cunning. In this enthralling game, players strategically remove numbers from a unique set: the odd numbers 1, 7, 9, 11, 13, 15, and so on. As the game unfolds, the players orchestrate a symphony of calculated moves, vying for the prized trinket of victory. This blog post delves into the nuances of the game's rules, the strategies at play, and the captivating interplay between two human minds that transform each decision into a pivotal moment.
**The Game Setup**
The heart of this strategic dance lies in the interaction between two human players. As the curtain rises, the game takes shape with the following rules:
- Human Player 1 and Human Player 2 alternate turns, removing numbers from the central board.
- Player 1 starts by selecting a number from the available choices.
- Player 2 continues the rhythm by picking numbers from the remaining options.
- The game marches on until a mere three numbers remain on the board.
**The Final Battle: Trinket Determination**
The crescendo of the game arrives with just three numbers left standing. In this pivotal moment, the total sum of these three digits takes center stage. If this sum is a multiple of 3, Human Player 2 emerges as the victor, claiming the coveted trinket. On the other hand, if the sum defies the rule of threes, the honor goes to Human Player 1.
**Strategic Moves and Human Wit**
At the core of the game's allure lies the intricate art of strategy, guided solely by the minds of the players. Two distinct strategies are at play:
1. **Blocker Strategy**: A player deploying the Blocker strategy aims to thwart their opponent's chances of achieving a multiple of 3. By meticulously selecting numbers, the Blocker strategy seeks to obstruct the path to victory, setting the stage for a triumphant conclusion.
2. **Strategist Approach**: Embracing the role of the strategist, a player assesses the ever-evolving board, evaluates potential moves, and anticipates future scenarios. This approach aims to ensure a winning position by making informed, calculated decisions.
**Code of the Mind**
The game's mechanics and strategic essence are abstractly implemented through human decision-making processes. Instead of lines of code, it's the players' mental algorithms that drive the gameplay. As each player contemplates their moves, they introduce an element of unpredictability and analysis, showcasing the true depth of strategic reasoning.
**Conclusion**
In the immersive realm of the 2-player card game, participants embark on a journey where strategy and intellect intertwine. With each move, players navigate a landscape of calculations and predictions, fueled by the desire to outmaneuver their counterpart and seize victory. The game encapsulates the essence of strategic thinking, underscoring the dynamic synergy between mathematical reasoning, gameplay dynamics, and strategic decision-making.
The next time you find yourself pondering your move in this captivating card game, remember that you're engaging in a duel of minds. Your choices are the brushstrokes that paint a masterpiece of strategy, where every calculated decision holds the power to shape the course of the game.
Research
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Frequently Asked Questions: The 2-Player Sum Number Card Game
1. What is the objective of this 2-player card game?
The objective of the game is for two players to take turns removing numbers (initially from the set 1 to 9) until only three numbers remain. Player 2 wins if the sum of these final three numbers is a multiple of three. Otherwise, Player 1 wins.
2. How is the game played?
The game begins with the numbers 1 through 9 (or a different set of numbers, as suggested by one source using odd numbers). Player 1 starts by choosing and removing one number. Player 2 then chooses and removes a different number from those remaining. The players continue to alternate turns, each removing one number at a time. This process continues until only three numbers are left on the board.
3. How is the winner determined?
Once only three numbers remain, their sum is calculated. If this sum is a multiple of 3 (i.e., the remainder when divided by 3 is zero), Player 2 wins. If the sum is not a multiple of 3, then Player 1 wins. In some versions or variations, Player 2's winning condition might be described as the "remainder of the sum of the last 3 cards is multiples of three," which means the same thing.
4. What role does strategy play in this game?
Strategy is crucial for both players. Player 1 might aim to leave a final set of three numbers whose sum is not a multiple of 3. Conversely, Player 2 will try to ensure that the final three numbers sum to a multiple of 3. This involves anticipating the opponent's moves and making choices that push the game towards their desired outcome. The sources mention "Blocker Strategy" (preventing the opponent's win) and "Strategist Approach" (planning moves to achieve a win).
5. Is this game intended for a specific educational purpose?
Yes, the sources indicate that this game is designed to help students gain a better understanding of basic mathematical operations, particularly addition and potentially subtraction (although subtraction is not explicitly mentioned in the win condition). It also implicitly involves understanding the concept of multiples. The game can be used as a simple and engaging way to reinforce these mathematical concepts.
6. Are there variations of this game?
One source excerpt describes a game played with a set of odd numbers (1, 7, 9, 11, 13, 15, and so on), suggesting that the initial set of numbers can be different. While the core mechanic of alternating turns and determining the winner based on the sum of the remaining three numbers being a multiple of three seems consistent, the specific numbers used can vary.
7. Is there a digital or app version of this game available?
Yes, the sources mention a "King Trikan 2 Players, Sum Number HOT SEAT CARD Game JavaScript HTML5 Applet by Theresa." An embeddable version of a "Sum Number Game" applet is also provided, indicating that the game has been developed as an interactive digital resource likely accessible through a web browser.
8. Who are the creators and contributors to this game?
The original idea for the game is attributed to Theresa Heng. Shaun Quek and Loo Kang Wee are credited with further development and compilation, as mentioned in the context of a version using EJS (Easy JavaScript Simulations) software. The "King Trikan" applet is also credited to Theresa, with Shaun Quek listed under "Mathematics."
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