The Beermat Puzzle

Recently I was cleaning out my garage I happened upon a photocopy of a submission I made to Computer & Video Games magazine. That was the first issue of the magazine which I purchased in 1981. The magazine had a cover attraction/competition taped to the front of four Octagons, I call them Beermats, details later. The magazine ceased publication early this decade. The Beermats constitute a puzzle and was designed by an expert in the field of puzzles - James Dalgety (his website - Pentangle Puzzles And Games has been temporarily closed but his other site - The Puzzle Museum is still accessible.

At the time of the magazine's launch personal computers were just climbing out of their primordial soup (or, more accurately sand in this case). At that time I owned my first computer - a Sharp MZ80K which had an integral monitor, not quite an iMac, a built in keyboard and a cassette tape drive (loading was slow but we had a lot of free time in those days) and Wow!!! - a whole 80K of memory!!!

I promptly threw myself into the design of a program which would check out all configurations of the Beermats to resolve the number of solutions where mirrored images were present on opposite connected faces - needless to say I didn't win the competition. The best three entries received a Commodore Vic20.

So what has that got to do with me? - you say.

Well, after unearthing my entry I proceeded to bring my solution up to date using my iPad and an excellent application - Codea (uses a Lua engine). Shortly after starting a number of forum members were asking for challenges/competitions so I decided to resurrect the puzzle in a new form (just different graphics using emojis). I cleared the use of the puzzle with James Dalgety as an educational challenge to the forum members and also checked it out with Future publishing (C&VG mag). So here we are - are you up to the challenge?

For those of you who haven't already jumped to another website - here are the details of the puzzle:

The puzzle consists of four double faced octogonal discs with eight edges per face. Each edge has two images associated with it. The object of the puzzle is to lay these discs down so that each disc contacts, face to face, with one of the other discs. The other discs can then be placed adjacent to the first two discs connecting at the edges/faces. When all four discs are aligned you effectively have a square. Most of these faces do not mirror those of the adjacent disc, but some do. In fact, to solve the puzzle you need to find a configuration of all four discs (all eight faces) which have mirrored images at each of the four interfaces. To achieve this you need to shuffle disc positions, flip sides and rotate them, presenting you with a range of faces opposite to those of the neighbouring discs.

How many configurations of the discs give matching (mirrored) images at each of the four connecting interfaces, produce a program to count them and to display the results. Easy - ehhhh? Actually - it takes a fair bit of thought and planning.

I am interested in seeing the approach that members take in solving the puzzle. It took me ages initially to solve the puzzle for the competition and twice as long to get it into Codea (largely because of my limited free time but also because, with new technology there are more ways to resolve and present the solutions).

At the time, the magazine used the speed of solution and program approach to judge the best entries - I don't think speed is a good criteria as the speed of computing varies significantly with the machine you own nowadays. Images of my updated discs have been provided on this website. If you don't have a computer you can still find the solution by printing out the images onto card, cutting out the discs and folding over at the common edge. I did this, used PVA glue and a few hours compression under a heavy flat surface, to get the discs to photograph the website header. Also to double check I had properly updated the discs and give my grandkids a few frustrating, but quiet hours, of entertainment. Skip to the Beermats link on the nav bar to see the discs.