Village Door Shuffle - A proposed New Problem
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This problem was inspired by a country walk with my wife and her sister. The shuffles and the brightly coloured village doors are real. Connecting the two to create the game described in the problem is, sadly, a figment of my imagination.
You are a very creative person. Whya don't you write a book like "Mathematics Can Be Fun" ? Appolgy if you already done that. :-)
Clive, thanks once more for the problem! It resembled me some article by Mike Gardner, probably called "Group Theory and Weaving Braids", but re-reading it doesn't help at least me to solve this at the moment :)
Sam's note actually hits what I'm thinking about for some time already: here are a number of good puzzles already created
by colleagues (with Clive's contribution for example amounting to over 50 problems of existing 400) - probably
it would be good to try compile such "selected" problems into a kind of plain pdf textbook - with the main goal of
preserving them in the case something unexpectedly bad may happen to the site (or rather myself).
Such a book could be updated time after time and supposedly should be distributed freely unless there are objections. As it is a vague idea yet, I'm open to any suggestions, from title to instruments to be used.
Sam, thank you for your kind thoughts. There are already an enormous number of "Maths can be fun" books out there and I don't feel particularly inclined to add to them. I do, however, take opportunities wherever possible to encourage other people to explore mathematical topics and to develop the thought processes needed to solve problems. My preferred kind of problem is one that requires only limited background knowledge but one where a considerable amount of thought is needed in order to reach a solution. The thought need not be entirely cerebral. There is a lot to be said for exploring ideas with pencil and paper, or writing programs to explore aspects of the problem before putting all of the pieces together. I have tried to vary the difficulty of the problems that I have submitted. Some of them should be soluble to anyone prepared to put in the necessary thought. Others are deliberately set to be more challenging. The hard ones don't get many solutions but I like to think that the people who have made it onto page 1 of the ranking list appreciate the occasional challenging problem. Certainly, some of Rodion's problems have been very challenging too.
As for the idea of creating a pdf document containing selected problems from the site, I can see no reason not to do this. However, I would expect it to contain all of the problems rather than a selection. There is so much excellent material on the site that it would be wrong to leave anything out. Unfortunately, the problems would lose a great deal if they were available only in this pdf format. Users could still solve the problems, using the examples given in the problem. But the examples are often simplified versions of the full problem, in order to provide useful test data for people trying to develop a full solution. There is certainly no obvious substitute for the website itself.