# Difference between revisions of "Infinite Defenestration"

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==Problem 2== | ==Problem 2== | ||

− | Prove that given <math>n</math> couples, you can defenestrate | + | Prove that given <math>n</math> couples, you can defenestrate <math>n</math> couples. |

==Problem 3== | ==Problem 3== | ||

Jim and his wife Jeri attend a party with 4 other married couples. As they enter, Jim and Jeri shake hands with some of the guests, but not with each other. During the evening, each person except 1 shakes hands with some of the guests, but not with their spouse. After the party, Jim asks each guest how many people they shook hands with and got answers 0,1,2,3,4,5,6,7,8. How many people did Jeri shake hands with? | Jim and his wife Jeri attend a party with 4 other married couples. As they enter, Jim and Jeri shake hands with some of the guests, but not with each other. During the evening, each person except 1 shakes hands with some of the guests, but not with their spouse. After the party, Jim asks each guest how many people they shook hands with and got answers 0,1,2,3,4,5,6,7,8. How many people did Jeri shake hands with? |

## Latest revision as of 20:30, 29 June 2022

**Infinite Defenestration** is a method of proof which utilizes repeatedly throwing members of a party out a window. It relies on that given people at a party, it is possible to throw member out the window, leaving members remaining.

## Contents

## Problem 1

Prove that given attendees of a party, one can defenestrate members.

### Solution

**Proof**

We use mathematical induction. We start with , which is trivial. We induct; give members defenestrated, remain. We throw out member, leaving us with members defenestrated and members remaining.

Thus lemma is true. Plugging in , we have

Try your hand at the following problems:

## Problem 2

Prove that given couples, you can defenestrate couples.

## Problem 3

Jim and his wife Jeri attend a party with 4 other married couples. As they enter, Jim and Jeri shake hands with some of the guests, but not with each other. During the evening, each person except 1 shakes hands with some of the guests, but not with their spouse. After the party, Jim asks each guest how many people they shook hands with and got answers 0,1,2,3,4,5,6,7,8. How many people did Jeri shake hands with?