"Back from the Klondike" Solution

6/25/2016

Loyd's given solution to the puzzle is to move southwest twice, northeast three times, southwest three times and end with what Loyd calls a "bold strike via southeast. to liberty!".

In 1976, two graduate students at the University of Washington wrote a Fortran program to solve the puzzle, and discovered hundreds of possible solutions, all of them eventually converging on a square which was part of Loyd's given solution. All of these routes also passed through a particular square which was not part of Loyd's solution, suggesting an artist's error in drawing the original puzzle. Changing this square from a "2" to a "1" results in a puzzle which only has a single solution.

Further Reading:

http://en.wikipedia.org/wiki/Back_from_the_Klondike

http://en.wikipedia.org/wiki/Sam_Loyd

http://www.mathpuzzle.com/loyd/

http://www-history.mcs.st-and.ac.uk/Biographies/Loyd.html 

David

Can You Complete This Sentence?

6/24/2015

Complete the following sentence by spelling out a number to make the statement true.

"This sentence contains _____________ letters."

David

A Puzzle From H. E. Dudeney

6/23/2015

Here is a problem published by Henry Ernest Dudeney in his book “Amusements in Mathematics” published in 1917.  He does not claim authorship of this problem.  He notes that Houdini used to use this problem, but he does not know who the author is.

Dudeney states: “The puzzle is to draw with three strokes of the pencil the diagram that the little girl is exhibiting in the illustration.  Of course, you must not remove your pencil from the paper during a stroke or go over the same line a second time.” 

“You will find that you can get in a good deal of the figure with one continuous stroke, but it always appear as if four strokes are necessary.”

I was not familiar with this problem until I read Dudeney’s book.  I have seen this diagram before, but the problem was stated differently.  As I recall, it is a diagram show the floor plan of a house with 5 rooms.  Each room has a doorway to enter any adjacent room, and a doorway to the outside of the house in every wall that borders the outside of the house.  The goal is to find a route to visit each room in the house just one.  You do not have to pass through every doorway, but the doorways you do pass through can only be used one.  My question is “Is there a solution to this problem?”

David