Imagine you’re a top spy working for Sausage Saloon. Your mission is to find the secret sauce recipe of Pasta Palace, which is hidden in a bank vault. But there’s a twist! Burger Bazaar has kidnapped one of Pasta Palace’s top chefs to extract the recipe’s location. Your job is to outsmart them and get the recipe first.
You’ve tracked down the place where the chef is being held. From your hiding spot, you watch as an interrogator questions the chef. The interrogator asks, “Is the number of the safe deposit box less than 500?” You can’t hear the chef’s answer, but you can tell he’s lying. The interrogator believes him anyway. Next, the interrogator asks, “Is it a perfect square?” Again, the chef lies, but the interrogator believes him. Finally, the interrogator asks, “Is it a perfect cube?” This time, the chef tells the truth. The interrogator seems satisfied and leaves to retrieve the recipe.
Now it’s your turn to solve the mystery. You know the interrogator has the wrong number, but can you figure out the right one? Let’s break it down:
To solve this, we need to find a number that is both a perfect square and a perfect cube, and is less than 500. The only number that fits all these conditions is 64. It’s the only number under 500 that is both a square (8×8) and a cube (4x4x4).
With this information, you retrieve the secret recipe and make your escape before anyone realizes what’s happened. You’ve successfully completed your mission!
Solving puzzles like this can be a fun way to practice logical thinking and problem-solving skills. Keep challenging yourself with more riddles and see how quickly you can crack the code!
Imagine you’re the spy in the story. Pair up with a classmate and take turns playing the roles of the interrogator and the chef. Practice asking and answering questions about the secret number, using clues from the article. Remember, the chef lies about some questions, so think carefully about your responses!
Use the structure of the secret sauce riddle to create your own puzzle. Think of a number and come up with a series of clues that involve mathematical properties like being a perfect square or cube. Share your riddle with the class and see who can solve it first!
Work in small groups to solve a series of math-based riddles. Each riddle will give you a clue to a final mystery number. Use your problem-solving skills to crack the code and find the secret number before time runs out!
Go on a scavenger hunt around the classroom or school to find objects that represent perfect squares and perfect cubes. For example, a 4×4 tile floor represents a perfect square. Document your findings and explain why each object fits the criteria.
Imagine you’re a spy like in the article. Design a gadget that would help you solve riddles and puzzles. Draw your gadget and write a short description of how it works and how it would help you in your mission to find the secret sauce recipe.
Here’s a sanitized version of the transcript:
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One of the top chefs from Pasta Palace has been taken by operatives from Burger Bazaar, who are trying to discover the location of their secret sauce recipe. Unbeknownst to them, a third party—Sausage Saloon—has sent you to take advantage of the situation. As their top spy, your skills include infiltration, subterfuge, safecracking, and reading faces for signs of deception.
You’ve tracked the captors to where they’re holding the chef. From your hiding spot, you can see him on the other side of the glass, while an interrogator wearing headphones speaks into a microphone. “We already know the recipe is on the 13th floor of the bank vault, in a safe deposit box numbered between 13 and 1300. Now tell us… Is the number less than 500?” You can’t hear the chef’s answer, but you can see that he’s not being truthful. The interrogator, however, believes him. He follows up by asking, “Is it a perfect square?” Again, you can’t hear the answer but can tell the chef is not being truthful, while the interrogator takes him at his word. He then asks, “Is it a perfect cube?” This time, the chef answers truthfully. The interrogator thinks for a moment and says, “Good. Now if you just tell me whether or not the number’s second digit is a one, we’ll be done here.” But as the chef starts to answer, the interrogator stands up, blocking your view. Moments later, he rushes out of the room, announcing that he has the answer and is sending agents to retrieve the recipe.
You know that the Burger Bazaar team has the wrong box number. But can you figure out the right one and retrieve the recipe yourself? Pause the video to figure it out for yourself.
The key here is to work backwards. We don’t know what the chef answers to the final question or whether he answers truthfully. However, by the time the interrogator asks it, he has narrowed the options down to two numbers—one where the second digit is 1, and one where it isn’t. Our goal is to find answers to the previous questions that lead to just two possibilities.
Of the three constraints offered, the one that narrows our options the most is if the number is a perfect cube. That leaves us with only eight answers between 13 and 1300. Let’s assume the answer to the third question was a truthful YES. Now, let’s look at the second question. If the chef answered YES to the number being a perfect square, it would narrow the interrogator’s options to just 64 and 729—the only numbers in our range that are both a square and a cube. But neither of these has a 1 as the second digit. So the answer to the second question must have been NO. This means we can eliminate these two squares from the interrogator’s list, leaving only six numbers.
Now for the first question, which allows us to divide this list. If the chef answered YES to the number being less than 500, we’d have four options, which is too many. But a NO leaves us with two numbers greater than 500, one of which does have a 1 as its second digit. We don’t know which of these numbers the interrogator thinks is correct. But that doesn’t matter—his conclusion was based on lies.
You, on the other hand, are now in a position to reconstruct the truth. First, the chef said the number was greater than 500 but lied, meaning it’s actually less than 500. Second, the chef said it wasn’t a perfect square but lied again, meaning the number is indeed a square. Finally, he truthfully confirmed that it was also a cube. As we’ve already seen, the only number under 500 that’s both a square and a cube is 64.
You find the secret recipe and are gone before anyone notices. Corporate espionage is not an easy game—but sometimes, that’s just how things unfold.
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This version maintains the essence of the original transcript while removing any potentially sensitive or inappropriate content.
Number – A mathematical object used to count, measure, and label. – Example sentence: The number 7 is a prime number because it has no divisors other than 1 and itself.
Perfect – A term used to describe a number that is equal to the sum of its proper divisors, excluding itself. – Example sentence: The number 28 is a perfect number because its divisors, 1, 2, 4, 7, and 14, add up to 28.
Square – The result of multiplying a number by itself. – Example sentence: The square of 5 is 25 because 5 times 5 equals 25.
Cube – The result of multiplying a number by itself twice. – Example sentence: The cube of 3 is 27 because 3 times 3 times 3 equals 27.
Less – Used to indicate that one quantity is smaller than another. – Example sentence: In the inequality 4 < 6, the number 4 is less than 6.
Than – Used in comparisons to indicate difference in quantity or degree. – Example sentence: The expression 8 is greater than 5 means that 8 is larger in value compared to 5.
Find – To determine a value or solution through calculation or reasoning. – Example sentence: To find the value of x in the equation 2x + 3 = 11, you need to solve for x.
Conditions – Specific requirements or constraints that must be met in a mathematical problem. – Example sentence: The conditions for solving the equation include that x must be a positive integer.
Logical – Relating to clear, sound reasoning, often used in problem-solving. – Example sentence: Using logical steps, we can solve the equation by isolating the variable on one side.
Skills – The abilities or expertise needed to perform mathematical tasks effectively. – Example sentence: Developing algebraic skills is important for solving complex equations and understanding functions.
