So, I’m teaching a new course, Math 2033, Mathematical Thought, and it’s going great! I’d like to take a moment to write about it!
(This is one reason the MF has been kinda slow lately; another is that I’m chair) When it’s fully up and running, we’ll have about 150 students in one large section each semester (we’re starting with about 100). In a nutshell, it’s the Math Factor, as a course.
In Living With Crazy Buttocks I posed a problem where 20 party guests were each given an unusual book. These books were placed in identical boxes. The guests enter the room with the boxes one at a time and are allowed to open half of the boxes. They leave by a different door and cannot communicate with the other guests. The room is put back identically before the next guest enters.
If every guest finds their book then the whole group win a trip to Paris.
What is their best strategy?
Michael Huber discusses the mathematics of the Twelve Labors of Hercules!
Recently I discovered Stan Wagon’s Problem of the Week. This is a delightful mailing list / site and some of the problems are in the vein of puzzles I post here. Recent problem 1125 captured the attention of several Math Factor authors so I thought I’d post the puzzle here as an excuse to introduce you all to that list.
You have eight batteries and know that four are good and four are dead, but don’t know which are which. Your only method of testing them is to insert two into a device that will work if you’ve put in two good batteries and not otherwise. How many such “tests” are required in order to be sure that you’ve located two good batteries?
As of this posting, the answer to this question is not yet on the POTW website, but if you come to this later, the spoiler may be there, so be careful to avoid spoilers if you want to work this through.
Finding yourself chatting around the water cooler one afternoon, you and two co-workers agree that you would all like to know the average of your three salaries but none of you want your individual salary to be known to either of the other two. Without need of involving any external person or machine as some sort of secret keeper, how can you achieve this end?
Janine is one of twenty guests at a Christmas party. Each guest is given a book as a present. Janines’s book is called ‘Living with Crazy Buttocks’. She isn’t sure what to make of that.
The guests are invited to play a game. Each book is put into an identical cardboard box. The boxes can be opened and closed without leaving a mark. The twenty boxes are piled up around the Christmas Tree.
The guests are told that they will each have the opportunity to open half of the boxes. Their objective is to find their own book. If they all succeed the group wins and they will win a trip to Paris. If any one of them fails then the group fails but they will each get a Twinkie to keep for life.
The guests are taken to another room and then taken to the tree one at a time. They cannot see what any other guest does at the tree. They are not able to communicate once the game starts. The boxes are put back after each guest, as though they had never been there.
You would think that the chance of the group succeeding was 1/2^20 but they can do much better than that.
The group must come up with a strategy before the game starts. What is the best strategy to get the group to Paris, and let Janine keep her ‘Crazy Buttocks’?
These books are all real. They will be helpful to you if you have had any of the following thoughts:
We all know the Nazis killed millions of innocent people but what were they like on ecological issues?
I would like to speak Italian but can’t be bothered to learn any Italian words, can you help?
Aubergines are very flushed, just how angry are they?
I think I’m dead, how can I tell for certain?
I am rich but dead. How should I pimp my coffin?
I am worried about running into large, slow moving objects; can you suggest any strategies to avoid this?
Just how boring was 1587?
I live thousands of miles from Versailles. Will I get a good view?
I am English, am I human?
My buttocks are insane.
Paul Nahin discusses his fabulous new book “Mrs Perkins Electric Quilt“, mosquitos, falling through the Earth, whether mathematics is “real” and much more!
There are five holes in a row in my yard. A fox lives in them moving around as follows: Each night, it abandons it current residence and moves to an immediately neighboring hole. If I’m allowed to check one hole each morning, identify a sequence of holes that I can check in order to be sure to catch the fox.
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