Math Problem Statement

You’ve been kidnapped by the evil wizard’s henchmen and taken to his secret tower as a prisoner. You are thrown into a dungeon cell, and in the cell you find a cruel riddle. In your cell is a magical scale with three balance pans. Whenever you place a single object in each pan, the scale tips to reveal the object with the median weight of the set of all three objects placed onto the magical scale. In your cell you also find a bag with 10 fluffy white feathers. The feathers are all slightly different in size, but because they’re so light, you can’t distinguish between their weights by hand.

The only way to bypass the enchanted lock on your cell and escape from the wizard’s tower is to place the lightest of the feathers in a small receptacle by the cell door. If you place the lightest feather, you will be set free. If you place any other feather, a sudden burst of magical flame will turn you into a pile of ash!

Imagine you have a magical scale and a collection of feathers. The scale has the unique ability to compare three feathers at a time and reveal the one that is of medium weight among them.

To use the scale effectively, you randomly select three feathers from your collection. If two of the feathers happen to be the same, you pick another one until all three are different. Once you have three distinct feathers, you place them on the scale. The scale then reveals the feather with the medium weight.

After identifying the feather with the median weight, you remove it from your collection, leaving you with fewer feathers. You repeat this process of selecting and weighing until only two feathers remain. At this point, you stop, and those two feathers are all that’s left from the original collection.

The goal of this method is to gradually reduce the number of feathers in your collection by consistently eliminating the one with the median weight, until you are left with just two feathers.

You don't know how long you have before the evil wizard arrives to carry out his undoubtedly nefarious plans for you, so you want to make your escape attempt as soon as possible. What is the minimum number of times you should call your function using_the_magic_scale so that you still maximize your chance of escape, and what will your chance of escape be?

A) 3, 100% B) 2, 66% C) 10, 100% D) 1, 50%

Solution

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Math Problem Analysis

Mathematical Concepts

Median
Probability

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9