The Mirzakhani wand, a fabled magical item, is said to be the most powerful ever created. This is why the evil wizard Moldevort plans to use it to conquer the world. Alongside Drumbledrore, you have finally discovered its hiding place within a cave. The wand is hidden by a system of 100 magical stones, including a glowing keystone, and 100 platforms. If the keystone is placed on the correct platform, the wand will be revealed. However, if placed incorrectly, the entire cave will collapse.
The keystone is immune to all magic, but the other stones aren’t. This means you can pick them up and cast a placement spell, and the platform that the stone belongs on will glow. If all 99 stones are placed correctly, the final platform must be the keystone’s correct resting place. However, just as you’re about to get started, one of Moldevort’s henchmen arrives and irreversibly seals a random stone to a random platform. If you need to place a stone that belongs on a platform that’s already occupied, your spell will make some random unoccupied platform glow instead. This poses the question: what are your odds of placing the keystone on the correct platform?
Let’s imagine we knew everything about this situation. With perfect knowledge, we could label the stones 1 to 100, based on the order we plan to place them and label the platforms they belong on in the same way. We’ll label the stone the henchmen placed as 1, meaning it was supposed to go on platform 1, and the keystone as 100, belonging on platform 100. Of course, we don’t know which platform is which, so the numbering of the platforms is actually invisible to us.
There are three possibilities: one, the first stone was placed randomly onto its own platform, in which case, you’re guaranteed to succeed. Two, it was placed on the keystone’s platform and you’re doomed to fail. But most likely— scenario three— it was placed somewhere else. Suppose the henchman placed stone 1 on, say, platform 45. Then you’d place stone 2 on platform 2, 3 on 3, and so on, until you got to stone 45. Its platform being taken, a random platform would light up.
In other words, you’re playing a game where you have equal chances to win and lose, and some chance to delay the decisive moment. No matter how many times this process repeats, you’ll inevitably either place a stone on pedestal 1 or pedestal 100 before you reach the keystone. That’s all that determines whether you succeed or fail, and critically, the chances of those events are equal.
You’re debating whether it’s worth risking a 50/50 chance of a cave-in when Drumbledrore reveals his secret weapon: a rare felush felucious potion, which grants extraordinary luck for a brief period of time. There’s a 1 in 100 chance the keystone’s platform was taken by the first stone and you’ve lost already, but otherwise, you’ve got even odds to win or lose. And right now, you’re feeling lucky.
Using a computer or a calculator, simulate the scenario described in the article. Write a simple program or use a spreadsheet to randomly place the stones and determine the outcome. Repeat the simulation multiple times to observe the probability of success and failure. Discuss your findings with your classmates.
Divide into small groups and role-play the scenario. One student acts as Moldevort’s henchman, while others take turns placing the stones. Use numbered cards to represent the stones and platforms. Keep track of the outcomes and discuss the strategies used to maximize the chances of placing the keystone correctly.
Create a math puzzle based on the article. Design a series of questions that require solving probability problems related to the placement of the stones and the keystone. Exchange puzzles with your classmates and solve them. Discuss the solutions and the mathematical concepts involved.
Write a short story or a diary entry from the perspective of Drumbledrore or one of the students. Describe the emotions, thoughts, and strategies involved in the quest to place the keystone correctly. Share your story with the class and discuss the different approaches taken by each character.
Create an artistic representation of the cave, the magical stones, and the platforms. Use materials like clay, paper, or digital tools to build a model or a drawing. Label the stones and platforms, and illustrate the process of placing the stones. Present your artwork to the class and explain the significance of each element in the context of the article.
Magical stones – Stones imbued with magical properties or abilities. – The ancient wizard used magical stones to harness the power of the elements.
Glowing keystone – A radiant stone that serves as a central element in a magical structure or spell. – The glowing keystone pulsated with an otherworldly energy, illuminating the entire room.
Platforms – Raised surfaces or stages that provide a base for people or objects. – The performers gracefully danced and twirled on the platforms, captivating the audience.
Placement spell – A magical incantation or ritual used to position or locate objects or beings. – The witch chanted the placement spell, causing the lost book to appear right in front of her.
Odds – The chances or probability of a certain outcome or event occurring. – The odds of winning the lottery are incredibly slim, but someone has to win eventually.
Perfect knowledge – A complete understanding or awareness of all relevant information or facts. – The wise old sage seemed to possess perfect knowledge of ancient legends and forgotten lore.
Possibilities – Potential options, opportunities, or outcomes that may occur. – The endless possibilities of the future filled her with excitement and anticipation.
Game of chance – An activity or competition where the outcome is determined by luck or random factors. – The roulette table at the casino is a classic game of chance, where players hope for the luck of the draw.
Cave-in – The collapse or falling in of a cave or underground structure. – The miners narrowly escaped the cave-in, but their path back to the surface was now blocked.
Luck – The force that brings about favorable or unfavorable events by chance. – She attributed her success to good luck, as everything seemed to go her way that day.
