# Cake Division Puzzle: Max Amount for 1st Person

• WilcoRogers
In summary: The first person then chooses his piece of cake #1. So the first person will get k, which is the largest piece of cake #1 he can get.In summary, the first person can get a maximum of k amount of cake by dividing the first cake into two pieces, with one piece being of size k and the other being of size 1-k, and then choosing the smaller piece. This strategy ensures that the first person gets the largest possible piece of cake #1.
WilcoRogers

## Homework Statement

Suppose that two people are dividing two cakes using the following rules:
1. The first person divides the first cake into two pieces in any fashion.
2. The second person then chooses which of the two cakes they will get to choose the first piece from.
3. The first person then cuts the second cake into two pieces in any fashion.
4. The second person chooses his piece of whichever cake he chose in step 2.
5. The first person chooses his piece of the other cake.

Devise a strategy that gives the first person as much cake as possible and say what that maximum amount is. Assume both cakes are the same size.

## The Attempt at a Solution

The idea I think is multivariate calculus, seeing as that's what we are studying at the moment, but I also think this is just my prof being clever... I figured not cutting the cake at all would allow the first person a whole cake no matter what, but I'm not sure if that's allowed. Has anyone seen this before?

Nobody has any idea?

Suppose the first cake is divided in 2 pieces of size k and 1-k with k<=1/2

If the second person chooses the first cake, he can get the largest piece of cake #1. He won't get anything of cake #2 because the first person can divide AND choose. So the second person ends up with (1-k)

If the second person chooses cake #2 he can get the smallest piece of cake #1 and half of cake #2, so the second person gets (1/2)+k

## What is the "Cake Division Puzzle: Max Amount for 1st Person"?

The "Cake Division Puzzle: Max Amount for 1st Person" is a mathematical problem that involves dividing a cake into equal parts and determining the maximum amount of cake that the first person can receive, given certain constraints.

## What are the constraints in the "Cake Division Puzzle: Max Amount for 1st Person"?

The constraints in the "Cake Division Puzzle: Max Amount for 1st Person" include the number of people involved, the total number of cake slices, and any other specific limitations set by the problem.

## How do you solve the "Cake Division Puzzle: Max Amount for 1st Person"?

To solve the "Cake Division Puzzle: Max Amount for 1st Person", you will need to use mathematical principles such as division, fractions, and logic. There are various strategies and formulas that can be used, depending on the specific constraints of the problem.

## Why is the "Cake Division Puzzle: Max Amount for 1st Person" important?

The "Cake Division Puzzle: Max Amount for 1st Person" is a fun and challenging problem that can help improve critical thinking and problem-solving skills. It can also have real-life applications in situations where resources need to be divided equally among a group of people.

## Are there variations of the "Cake Division Puzzle: Max Amount for 1st Person"?

Yes, there are various versions of the "Cake Division Puzzle: Max Amount for 1st Person" with different constraints and scenarios. Some may involve dividing a cake into different shapes or using different mathematical operations. The key principles and strategies remain the same, but the specific solutions may differ.

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