The city has recently unveiled its unique Fabergé Egg Museum, a towering 100-story building with a single, exquisite egg displayed on each floor. These eggs, identical in weight and construction, increase in rarity and value as you ascend the building. Naturally, this has caught the attention of the world’s most infamous jewel thief, who is eyeing the ultimate prize.
Given the tight security and the substantial size of the eggs, the thief can only attempt to steal one by dropping it out of a window into her waiting truck and then rappelling down before the authorities arrive. Her challenge is to determine the highest floor from which an egg can be dropped without breaking, as she suspects the top floor’s egg won’t survive a 100-story fall. To achieve this, she plans to use two souvenir eggs from the museum’s gift shop—perfect replicas but utterly worthless—to conduct her tests.
The thief’s goal is to find the highest floor where an egg can survive the fall with the fewest number of attempts. If she only had one replica egg, she would have to start from the first floor and work her way up, potentially requiring up to 100 tries. However, with two eggs, she can employ a more efficient strategy.
By dropping the first egg from various floors at larger intervals, she can narrow down the range where the critical floor might be. Once the first egg breaks, she can use the second egg to test each floor within that range. While large intervals might seem efficient, they could lead to numerous tests with the second egg. Smaller intervals, however, offer a better solution.
For instance, if she starts by dropping the first egg from every 10th floor, she would only need to test the nine floors below once it breaks, resulting in a maximum of 19 tries. But can she improve this strategy further?
Indeed, by varying the interval sizes, she can minimize the number of attempts. If the building had only ten floors, she could test it with just four throws by dropping the first egg at floors four, seven, and nine. Depending on where the first egg breaks, she would need up to three additional throws with the second egg to pinpoint the exact floor.
The key is to divide the building into sections where, regardless of the correct floor, it takes the same number of throws to find it. Each interval should be one floor smaller than the last. By solving this equation, the thief can determine the optimal starting floor in the 100-story building.
Through trial and error, she finds that starting on the 14th floor and moving up to the 27th, 39th, and so on, allows her to complete the task in a maximum of 14 drops. As the old saying goes, you can’t pull a heist without breaking a few eggs.
In conclusion, the thief’s meticulous planning and strategic approach highlight the art of the perfect heist, where precision and calculation are as valuable as the prize itself.
Imagine you are the thief planning the heist. Create a simulation using a spreadsheet or a simple coding tool like Scratch. Drop the eggs from different floors and record the results to find the highest floor an egg can survive. Share your findings with the class.
Work in pairs to play a game where you have to determine the highest safe floor using two eggs. Use a 100-square grid to represent the floors. Take turns dropping the eggs and marking the results. The goal is to find the optimal strategy with the fewest drops.
Write a short story from the perspective of the thief. Describe her thought process, the challenges she faces, and how she uses math and logic to plan the heist. Illustrate your story with diagrams showing the egg drop strategy.
Conduct a real-life egg drop experiment. Use different materials to create protective casings for the eggs and drop them from various heights. Record which designs work best and discuss how this relates to the thief’s strategy in the article.
Solve a series of math problems related to the egg drop scenario. Calculate the optimal floors to drop the eggs from in buildings of different heights. Present your solutions and explain the reasoning behind your calculations.
Egg – An oval shape commonly studied in geometry for understanding curves and areas. – The egg shape is useful in demonstrating how certain curves are formed in mathematics.
Floor – The base surface of a room, often referenced in geometry when discussing areas and dimensions. – For our math project, we calculated the floor area to determine the number of tiles required.
Drop – The action of letting something fall, frequently analyzed in physics and mathematics to explore gravity and motion. – By dropping a ball from a certain height, we can calculate the time it takes to reach the ground.
Attempts – The repeated effort to achieve something, particularly in problem-solving. – After multiple attempts to solve the math problem, I finally arrived at the correct solution.
Strategy – A planned approach designed to achieve a specific goal, especially in tackling problems. – We formulated a strategy for the math test by reviewing essential concepts and practicing problems.
Optimize – To enhance or improve a method to achieve the best possible outcome, particularly in solving equations. – We need to optimize our method for solving the equation to find the quickest solution.
Interval – A span of values or time, often used in mathematics to describe the distance between two points. – Understanding the interval between the two numbers on the number line helps us comprehend their relationship.
Test – An evaluation intended to gauge a person’s knowledge, skills, or abilities, especially in academic subjects. – I prepared thoroughly for the math test to ensure I could accurately solve all the problems.
Solve – To find a solution or answer to a problem, equation, or puzzle. – I successfully solved the equation by isolating the variable on one side.
Calculation – The process of using mathematical methods to determine an answer, especially involving numbers or quantities. – My calculation revealed that the total cost of the items was lower than I had anticipated.
