In the world of wizardry, being chosen as a champion to represent your house in a magical duel is both an honor and a perilous challenge. This duel pits you against formidable opponents from two rival magic schools, each wielding powerful wands with unique abilities. The key to victory lies not only in the wand you choose but also in the strategy you employ.
Your first opponent hails from the Newt-niz school, wielding a wand that can transform people into fish with a 70% success rate. The second opponent, from the Leib-ton school, possesses a wand that turns people into statues, boasting a 90% effectiveness. The duel follows a strict order: you cast first, followed by the Newt-niz magician, and then the Leib-ton enchantress. This sequence repeats until only one wizard remains standing. To prevent a draw, if all participants are still standing after the first round, everyone will be turned into cats.
Your wizarding house offers you three wand options:
Initially, the Noether 9000 seems like the obvious choice due to its perfect accuracy. However, wielding the most powerful wand makes you the primary target for both opponents. After eliminating the most dangerous opponent, there’s still a 70% chance of being defeated by the remaining wizard.
Considering the Gaussian wand, which works 80% of the time, you realize that you wouldn’t become a target until the enchantress is incapacitated. However, transforming her would likely result in being turned into a fish by the sorcerer. If you target the sorcerer, the enchantress would almost certainly turn you to stone. Missing on purpose with the Gaussian could lead to the sorcerer attacking the enchantress, giving you an 80% chance of winning against him.
Yet, there’s a flaw in this plan: the sorcerer might also pass his turn, forcing the enchantress to cast her spell on you, the more dangerous opponent. This realization leads to a surprising strategy: choose the weakest wand, the Bannekar, and intentionally miss your first shot.
By missing on purpose with the Bannekar, the sorcerer becomes the enchantress’s target, compelling him to attempt to turn her into a fish. With a 70% success rate, he might succeed, leaving you with a 60% chance of winning the duel in the next round. If he fails, he risks being turned to stone, and you still have a 60% chance of defeating the enchantress. Although there’s a slim 3% chance of all participants being turned into cats, this strategy offers better than even odds of victory.
In the end, the best way to secure your win is to strategically throw away your shot, leveraging the weaknesses of your opponents and the rules of the duel to your advantage.
Form small groups and debate which wand you would choose and why. Consider the strengths and weaknesses of each wand and how they align with the strategies discussed in the article. Present your group’s decision and reasoning to the class.
Calculate the probability of winning the duel using each wand. Create a chart that shows the success rates of each wand and the likelihood of defeating each opponent. Discuss how these probabilities influence your strategy.
In pairs or small groups, role-play a magical duel using the wands and strategies from the article. Take turns casting spells and reacting according to the success rates provided. Reflect on how the strategies played out in practice.
Use a computer or tablet to simulate multiple rounds of the duel with different strategies. Record the outcomes and analyze which strategy yields the highest success rate. Share your findings with the class.
Write a short story from the perspective of a wizard participating in the duel. Describe your thoughts and feelings as you choose your wand and execute your strategy. Include the outcomes of each round and how you adapt your plan to achieve victory.
Wand – A stick or rod that is often used in magic or to represent power. – The magician waved his wand to make the rabbit disappear from the hat.
Strategy – A plan of action designed to achieve a specific goal. – In math competitions, having a good strategy can help you solve problems more quickly.
Success – The achievement of a goal or the accomplishment of something desired. – After studying hard for the math test, her success was evident when she received an A.
Opponents – <i.People or teams that compete against each other in a game or contest. – The math team faced tough opponents in the regional competition.
Chance – The likelihood or probability of something happening. – There is a good chance that you will solve the puzzle if you work together.
Target – A specific goal or objective that one aims to achieve. – Our target is to improve our math scores by 10% this semester.
Duel – A contest between two people or teams, often to settle a dispute. – The two students had a duel of wits during the math challenge.
Transform – <i.To change in form, appearance, or structure. – Learning new strategies can transform your approach to solving math problems.
Choose – <i.To select from a number of options. – You can choose any three problems to solve for extra credit in math class.
Magic – The use of special powers to make things happen that seem impossible. – In math, finding the right formula can feel like magic when it helps you solve a difficult problem.
