Interesting restricted tray-packers

A couple of weeks ago I managed to acquire a couple of rather interesting little restricted tray packing puzzles from Wil… and I managed to find some puzzling time earlier this week so I hauled them out and worked my way through them in between one of my other little projects. 
 

Pocket had been entered in the 2018 Nob Yoshigahara Puzzle Design Competition but I hadn’t been able to have a bash at it in San Diego – so when I saw a copy in one of Wil’s crates I pounced on it. Designed by Koichi Miura and MINE, my copy came with two sets of pieces, each of which needs to be inserted into the tray through the slot at the top… which holds the only little wrinkle: a single obstructing voxel.

The two sets of pieces appear to be a beginner’s puzzle and a slightly more advanced puzzle – with the beginner’s pieces all being made up of two pairs of blocky pieces (C’s and P’s – both hexominoes) and a little playing will convince you that there’s probably only really one way to arrange all of those pieces in the tray, so the puzzle reduces to finding a way to get them in there… as I said, I think this is the beginner’s challenge – in fact, it wasn’t even used in the Design Competition.

The second set of pieces provides a slightly trickier challenge: all four pieces are different and they all have 45 degree corners / cut-outs… which makes for a lot of interesting ways to combine them in the shape and size of the tray provided… sadly, however, most of those arrangements are precluded by that one, pesky little voxel sitting in the centre of the top slot… I should know, as I spent an awfully long time trying various arrangements that turned out to be un-assembleable. (It IS a word, now!). Finding the one that does work is quite a treat – it definitely rewards the solver in a delightful manner.

I hadn’t ever seen or heard about Packing Puzzle 4P until I stumbled across it at Peter’s place – I did recognise the designer’s name -  Hajime Katsumoto – and I have rather enjoyed a few of his other designs, so I took a punt and I ended up being rather glad I did.

There’s a two-sided tray, helpfully titled “Puzzle 1” and “Puzzle 2” and a set of four P-pentominoes… it’s pretty clear from the get-go that you need to put the four pieces into each of the (slightly obstructed) 4 * 5 frames. The holes on the first side are big enough to allow pieces to be inserted either way up, which is helpful… and you can fiddle around for a while and realise that you’re going to need to be a little creative in order to find a solution to this one… it’s quite a cute little solution and gives a nice little “A-Ha!” moment.

Puzzle 2 on the other hand is a bit of a sod – it kept me going for a lot longer! The holes on the second side are 5 voxels and P-shaped – so you can simply drop in the last two pieces, right?! Fine… all you need to do is position the first two pieces correctly and you’re done… except you can’t!  I spent ages trying variations on a theme, doing things this way and then that, and every single time I ended up with the same conclusion – it doesn’t work! Unless I can get one piece to magically pass THROUGH the other, they ain’t getting into the position I want them to be in…

Desperation led me to resort to Think(C)ing (it’s been a while!) and then even to consider CHEATing – although I did manage to stop myself just short of doing that when I realised I wouldn’t actually be able to UNDO the thing I was about to DO… until the right little briefest flash of inspiration struck and seconds later side 2 was solved – love it!

The last puzzle in this post turned out to be my first and second prize for A2P2 – each year my competition winners are invariably puzzle collectors who already “have everything” – so finding a puzzle they haven’t got turns into an annual conundrum for me… with Wil Strijbos invariably managing to turn up something SO NEW that nobody could possibly have a copy yet – Framed Jigsaw was that puzzle this year.

The original design comes courtesy of Hajime Katsumoto (yes there’s a spelling mistake on the puzzle... sorry) but it’s been “Streetwise’d” and “JCC’d” resulting in the improved version here – the pic shows the starting position with what appears to be a nicely checkered set of jigsaw pieces under a partial clear frame – with a central 2*2 hole… almost fully constructed – except for the final piece that obviously(!?) belongs in the top right hand corner – is the wrong colour for a neat checkerboard pattern, and has a tongue and a groove too many… which is odd.

Removing the pieces tells you a lot about how interesting this puzzle is going to be… a piece come out easily, but then you need to start moving things around to get the rest of the pieces out: the central opening is big enough for the 2*2 pieces, but not big enough for any tongues projecting outwards… so you need to manoeuvre pieces to be fully in the open frame in order to remove them – taking things out at an angle relative to the tray, isn’t possible at all…

Get all the pieces out and some things become apparent, like all tongues fit all grooves – and there are the same (ergo just enough) number of each…which is great: it means there are LOTS of ways of constructing a 4*4 square with those pieces.

How many of those do you think are assembleable (yup, still a word! Work with me here…)?

Very, very few!

You need to be able to keep as many degrees of freedom available as you progress or you’ll find yourself up a blind alley that simply won’t allow the last couple of pieces to be inserted… and let me tell you that I found a LOT of ways of almost doing this one…there is a solution to be found, and I found it quite tough – Nick on the other hand seemed to solve it rather rapidly, and I’m not sure how Ali’s doing/done… at least I know it wasn’t trivial! :-)