Imagine this: the evil Dr. Schrödinger has created a machine to make giant cats and plans to unleash them on the city! You and your team of secret agents have tracked him down to his hidden lab. But when you burst in, you realize it’s a trap! Dr. Schrödinger has escaped to another room to activate his device, and he’s disabled the control panel on his way out. Luckily, your team is full of skilled spies.
Agent Delta manages to hack into the control panel and get some of it working again. Meanwhile, Agent Epsilon finds the code you need to escape: 2, 10, 14. All you have to do is enter these numbers in order to unlock the door and stop Dr. Schrödinger.
Here’s the tricky part: the control panel only has three buttons. One adds 5 to the current number, another adds 7, and the third takes the square root of the number. You need to make the display show 2, 10, and 14, in that order. You can show other numbers in between, but you can’t repeat any number, show a number greater than 60, or display a non-whole number, or else the room will explode! Right now, the display shows zero, and time is ticking.
First, you need to figure out how to get to 2. Adding 5 or 7 increases the number, while the square root button decreases it. You realize that you can only use the square root button on perfect squares like 49, 16, or 36. You can’t make 4 or 16 directly with just the 5 and 7 buttons, so you aim for 36.
To reach 36, you press the buttons in this order: add 5, add 7, add 5, add 7, add 5, add 7. Then, you take the square root to get 6. Now, you add 5 twice to reach 16, and take the square root twice to finally get to 2. You’re on your way!
Next, you need to reach 10. You can’t get there directly by adding, so you aim for another perfect square. You add 7 to reach 9, then take the square root to get 3. Adding 7 again gives you 10.
Finally, you need to make the display show 14. You think about where you could be before reaching 14: either 7 or 9. Since you’ve already used 9, you aim for 7 by reaching 49 first. You carefully add five 5s and two 7s to reach 49, then take the square root to get 7. Adding 7 more gets you to 14, and the door opens!
Thanks to your quick thinking and problem-solving skills, you and your team stop Dr. Schrödinger’s plan just in time. As for Dr. Schrödinger, he’ll be spending some time in a box of his own, far away from his giant cat army!
Imagine you’re in the lab with the control panel in front of you. Use a calculator or a digital tool to simulate the button presses needed to solve the puzzle. Start from zero and try to reach 2, 10, and 14 in order, using the operations described. Record your steps and see if you can find a different solution path!
Research and list all perfect squares up to 60. Discuss with your classmates how these numbers can be used strategically in the puzzle. Why are perfect squares important in this challenge? Share your findings with the class.
Write a short story about what happens after you stop Dr. Schrödinger. How do you and your team celebrate? What happens to the giant cat army? Use your imagination and include some math-related elements in your story!
Create your own math puzzle using a similar concept. Design a control panel with different operations and set a new goal for your classmates to achieve. Make sure to include a clear set of rules and a solution. Exchange puzzles with a partner and try to solve each other’s challenges.
Work in small groups to solve the original puzzle. Each group member can take on a different role, such as the button presser, the strategist, or the recorder. Discuss your strategies and see which group can solve the puzzle the fastest. Reflect on what strategies worked best and why.
Here’s a sanitized version of the provided transcript:
—
The villainous Dr. Schrödinger has developed a growth ray and intends to create an army of giant cats to terrorize the city. Your team of secret agents has tracked him to his underground lab. You burst in to find that it’s a trap! Dr. Schrödinger has slipped into the next room to activate his device and disabled the control panel on the way out. Fortunately, your teammates are masters of spy-craft. Agent Delta has hacked into the control panel and managed to reactivate some of its functionality. Meanwhile, Agent Epsilon has searched through surveillance to find the code for the door: 2, 10, 14. All you have to do is enter those numbers, and you’ll be free.
But there’s a problem. The control panel has only three buttons: one which adds 5 to the display number, one which adds 7, and one which takes the square root. You need to make the display output the numbers 2, 10, and 14, in that order. It’s okay if it outputs different numbers in between, but there’s no way to reset the display, so once you get to 2, you’ll have to continue on to 10 and 14 from there. Not only that, Agent Delta explains that there are other traps built into the panel. If it ever shows the same number more than once, a number greater than 60, or a non-whole number, the room will explode. Right now, the display reads zero, and time is running out. There’s only one way to solve the puzzle, with a few small variations.
How will you input the code to escape from Dr. Schrödinger’s lair and save the day? Pause the video now if you want to figure it out for yourself!
You look over your options. Adding 5 or 7 increases the number, and the square root button will make it smaller. But there are only a few options where you can use that button: 49, 16, 36, and 49. You’d love to make 4 or 16. Then you could hit the square root button once or twice to get 2. But you can’t make either with just the 5 and 7 buttons.
You look at the other possible options for numbers you could take the square root of. Nine you can’t reach. Twenty-five and 49 would take you back to 5 or 7, and you can already get to each of those. Thirty-six is your only option. You add 5, 7, 5, 7, 5, 7, and then hit the square root button. Why that series of 5s and 7s? It’s somewhat arbitrary, but you know that you want to avoid 10, 14, and perfect squares since you’ll need them later. This gets you to 6.
Looking at your options, you see that 16 is now in your sights. You add 5 twice more to reach it. Then hit square root twice. That gets you to 2. You’re on your way! Now to 10. You can’t get straight there through addition alone, so you’re going to have to reach another square. Taking the square root of 9 or 25 would get you to a good place, but it turns out that 25 is unreachable from 2. So you add 7 to get to 9, then take the square root again. That gets you to 3. Adding 7 again makes 10.
Finally, you need to reach 14. Thinking backwards, you imagine where you could be before 14: 7 or 9. But 9 won’t work because you’ve already used 9. However, you could get to 7 by reaching 49 first. You add your way towards it, being careful not to hit any of the numbers you’ve hit so far. You thread your way carefully, adding five 5s and two 7s. Then, square root to 7, and add 7 more. The door opens, and you’re out of the trap.
Thanks to your problem-solving skills, your team gets Schrödinger’s cats out of the box in the nick of time. As for Schrödinger, you can be certain of one thing: he’ll be spending quite some time in a box of his own.
—
This version maintains the essence of the original transcript while ensuring clarity and appropriateness.
Numbers – Symbols or words used to represent quantities or values in mathematics. – In algebra, we often use letters to represent numbers in equations.
Add – To combine two or more quantities to get a sum. – When you add 5 and 3, you get 8.
Square – The result of multiplying a number by itself. – The square of 4 is 16 because 4 times 4 equals 16.
Root – A value that, when multiplied by itself a certain number of times, gives the original number. – The square root of 9 is 3 because 3 times 3 equals 9.
Perfect – A term used to describe a number that is the square of an integer. – 16 is a perfect square because it is 4 times 4.
Escape – To find a solution or way out of a mathematical problem. – To escape the complexity of the equation, we simplified it step by step.
Display – To show or exhibit mathematical data or results. – The graph was used to display the results of the algebraic equation.
Current – Referring to the present value or state in a mathematical process. – The current value of x in the equation is 5.
Order – The arrangement or sequence of numbers or terms in a particular way. – In order of operations, you must solve the equation inside the parentheses first.
Problem – A question or exercise in mathematics that requires a solution. – Solving the algebra problem took several steps to find the correct answer.
