Geometry / Mr. Hansen	Name: _______________________________________
10/29/2008

Mr. Hansen’s Umbrella Problem
An Example of Indirect Proof

Given:	Mr. Hansen drives to work. Mr. Hansen’s car does not have a keyless ignition option. Mr. Hansen has hooked his keys onto his umbrella, in his office.
Prove:	Mr. Hansen will not forget his umbrella at the office.
	The usual forgetfulness mode is to have the umbrella somewhere in the office or lying about and then simply to forget it at the end of the day. Hooking the keys to the umbrella disrupts this pattern. The proof is below.
Proof:	Assume (bwoc) that Mr. Hansen does forget his umbrella at the office. This is equivalent to saying that he will arrive home and discover that his umbrella is not with him. However, arriving home implies driving home. Driving implies using the keys. Using the keys implies removing them from the umbrella . This final step is a contradiction, since even though Mr. Hansen is sometimes absent-minded, he is not so absent-minded that he would unhook his keys from the umbrella and then leave the umbrella at work. (Maybe in a few years, but luckily, not yet . . .)