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?

Read the rest of this entry »

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.  

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.

I recently got back in touch with an old friend and puzzler and he reminded me of a puzzle that he once told me about that confounded me for weeks.  Faced with a restatement of it, again I couldn’t come up with an answer for the life of me.  The mechanism is painfully simple, but there is something about the particulars here that short my mind out.

Combine the four number 1,3,4,and 6 with operators of addition, subtraction, multiplication and division (and parenthesis to indicate order of operation) to yield an expression equal to 24.

I assure you that you can take this in the most straight-forward manner possible.  You aren’t mean to smoosh them together to get “13” out of 1 and 3.  You aren’t meant to use “1” as a problem number or something of that sort.  An answer will look something like this:

(4-1)*3/6

except that is equal to 1.5 .  Your expression must equal 24.

I’m interested to hear if this is as difficult for others as it was for me.

Hmm. Somehow Stephen Morris pulls off that rarest of Math Factor tricks– leaving Kyle and Chaim at a loss for words, with his sneaky clock puzzle.

Standard Podcast [ 6:38 ] Play Now | Play in Popup | Download

This will be the last of my Lewis Carroll posts.  In Pillow Problems, Carroll writes:

   Three Points are taken at random on an infinite Plane.  Find the chance of their being the vertices of an obtuse-angled Triangle.

Note: An obtuse-angled triangle is one that has an angle measuring more than 90 degrees.

Kyle and Chaim get into trouble with their wives and Mathfactor correspondent, Stephen Morris, discusses the Kate Bush Conjecture and And The Clocks Struck Thirteen  

Standard Podcast [ 10:33 ] Play Now | Play in Popup | Download

Oh by the way, would you like a cool Math Factor Poster? Click on this to download:

This puzzle is taken from a letter Carroll wrote to a 14-year-old girl named Helen Fielden.  Carroll writes:

I don’t know if you’re fond of puzzles, or not.  If you are, try this.  If not, never mind.  A gentlemen (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it — a square window, 3 feet high and 3 feet wide.  Now, he had weak eyes, and the window gave too much light, so (don’t you like “so” in a story?) he sent for the builder, and told hm to alter it, so as to give half the light.  Only, he was to keep it square — he was to keep it 3 feet high — and he was to keep it 3 feet wide.  How did he do it?  Remember, he wasn’t allowed to use curtains, or shutters, or coloured glass, or anything of that sort.