I don't normally spend too much time on a single puzzle, because I have many puzzles in my collection (a lot of them Exchange Puzzles) that I have yet to go through. From my last count from two exchanges, I have still over 140 more which are untouched. I know there are those who persist with a single puzzle for weeks at an end, eg Kevin Sadler and I truly respect their efforts! But I am not one of them.
But Square Dissection got more than my usual fair share of attention because firstly I quite like packing puzzles and secondly, I also enjoy designing them and producing working copies in plexiglass for myself or for sale. So when I selected Nick Baxter's Square Dissection from my stash, which was his IPP34 Exchange Puzzle, and thinking to myself that its JUST 9 ordinary rectangles into a tray, I decided to test my solving powers on his design....and failed quite miserably!
First the specs...the tray measures 9.5cm x 9.5cm x 0.6cm. The pieces are all rectangles with differing measurements for each like 18x20, 24x25 etc. These are not actual measurements but unit values of the length x width of the pieces. Both tray and pieces are made of translucent red and green acrylic/plexiglass. Everything is laser cut to perfection...and tight tolerances are indeed needed for this puzzle!
The goal is to place all the 9 green rectangles into the tray with none of the pieces sticking out. Your regular 2D tray packing puzzle right? Yes, but nothing regular about it. In fact after trying for several days on and off and not getting anywhere (there is always just one last piece that refuses to go in), I did what I usually advocate; that is to ask the designer for help. Nick came back with a series of questions which were actually hints on the solve. Needless to say, these hints were lost on me and another round of email exchanges resulted in yet more hints. Still no luck and a couple of weeks later, I threw in the towel and asked for the solution. Damn...everything fits so easily and nicely into the tray! Actually there is a bit more to this puzzle that meets the eye but I shan't mention anything more here as I don't want to have any spoilers for those who may still be tearing their hair out over the Square Dissection.
This puzzle may look innocuously ordinary, but there is a lot of "mathematics" behind the design and IMHO, very difficult and challenging. According to Nick, there are 23,224,320 ways to lay the pieces in a 3x3 format but only one will enable the correct fit inside the tray. And before I forget, don't waste your time with Burr Tools, it won't work.
For hardcore packing fans, this is a must have! Dave Holt, hope you are reading this. Go for one!