In a bleak dystopian world, your resistance group stands as humanity’s last hope. Captured by tyrannical rulers, you find yourselves in an ancient colosseum, destined to become part of their deadly entertainment. As you face this grim fate, a glimmer of hope emerges in the form of Zara, whose impeccable logical reasoning makes her the group’s best chance for survival.
Before being thrown into the dungeon, you notice numerous numbered hallways leading outside, each blocked by an electric barrier with a combination keypad. Only one of you will be given the chance to escape by solving a challenge, while the rest face a grim fate with mutant salamanders the following morning. Zara is chosen to attempt the escape, equipped with a concealed audio transmitter to keep the group informed.
As Zara is led away, her footsteps echo through one of the hallways before stopping. A voice announces the challenge: she must enter a code consisting of three positive whole numbers in ascending order. The second number must be greater than or equal to the first, and the third greater than or equal to the second. Zara is allowed to ask for up to three clues, but any wrong guess or unnecessary words will result in her being thrown back into the dungeon.
The first clue reveals that the product of the three numbers is 36. For the second clue, the voice states that the sum of the numbers matches the number of the hallway Zara entered. A tense silence follows, as Zara remembers the hallway number but cannot communicate it. Instead of entering the passcode, she requests the third clue, which reveals that the largest number appears only once in the combination.
Moments later, the electric barrier buzzes and stops, signaling Zara’s successful escape. However, her transmitter is now out of range, leaving you with limited information. Despite not knowing the hallway number, you decide to work through the clues from the beginning.
From the first clue, you deduce all eight possible combinations that result in a product of 36. The challenge lies in identifying the correct one. By calculating the sum of each combination’s numbers, you realize that all but two sums are unique. If the hallway number matched any unique sum, Zara would have known the correct combination without needing the third clue. Since she did ask for it, the hallway number must match the only sum that appears more than once: thirteen.
With two combinations adding up to thirteen—1, 6, 6 and 2, 2, 9—the third clue becomes crucial. It specifies that the largest number must be unique, confirming that 2, 2, 9 is the correct code. As night falls, you and the others escape through hallway thirteen, reuniting with Zara outside. Together, you have freed yourselves through the power of math and logic, ready to liberate the rest of the world.
Imagine you are Zara. Create your own puzzle similar to the one in the story. Choose a product and sum for three numbers, and write clues that lead to the solution. Share your puzzle with a classmate and see if they can solve it!
Form teams and set up a relay race where each team must solve a series of math and logic puzzles to advance. Use problems similar to the ones Zara faced, such as finding combinations of numbers that meet specific criteria. The first team to solve all puzzles and reach the finish line wins!
Write your own short story set in a dystopian world where the characters must use logic and math to survive. Include at least one puzzle or challenge that the characters must solve. Share your story with the class and discuss the different ways logic and math can be used in problem-solving.
Create a mini escape room in your classroom. Design puzzles and challenges based on the story, such as finding the correct combination of numbers to unlock a “door.” Work in small groups to solve the puzzles and escape the room within a set time limit.
Design a board game where players must solve math and logic puzzles to advance. Include different types of challenges, such as finding number combinations, solving riddles, and decoding clues. Play the game with your classmates and see who can reach the end first!
Logic – The study of correct reasoning and argumentation. – Logic helps us determine whether an argument is valid or not.
Numbers – Symbols used to represent quantities or values. – In math class, we learn how to add, subtract, multiply, and divide numbers.
Product – The result of multiplying two or more numbers together. – The product of 6 and 4 is 24.
Sum – The result of adding two or more numbers together. – The sum of 5 and 7 is 12.
Combination – A selection of items where the order does not matter. – The combination of 3 fruits from a basket of 5 can create different snack options.
Clues – Hints or pieces of information that help solve a problem. – In a math puzzle, the clues guide you to find the correct answer.
Unique – Being the only one of its kind; unlike anything else. – Each number in a set should be unique to avoid confusion in calculations.
Escape – To break free from a situation or constraint. – In a math game, you need to escape the maze by solving equations correctly.
Ascending – Arranging numbers or items in increasing order. – When we list the numbers 2, 5, and 1 in ascending order, we write 1, 2, 5.
Reasoning – The process of thinking about something in a logical way to form conclusions. – Good reasoning helps us solve complex math problems effectively.
