Tuesday 11 October 2011

P&L Packing Puzzle

The P&L was designed by Junichi Yananose and made and sold by Mr Puzzle Australia (aka Brian Young) for exchange at IPP31. It is actually a petite packing puzzle measuring 80mm(L) x 63mm(W) x 23mm(H) and very pocketable. Again the attraction for me to this puzzle was the use of 5 different woods consisting of Queensland Silly Oak, Tasmanian Blackwood, Pepperwood, Rosewood and Queensland Silver Ash. My copy is very well cut and made and all the pieces fit into the box very nicely.
The object of the puzzle is to pack into the box 5 L-shaped pieces and 5 P-shaped pieces. One of the L-shaped pieces has a No.31 (IPP31) on one of its surfaces and this No.31 must show up on top when the puzzle is in the solved state. The 10 pieces form two layers inside the box with no empty spaces. Externally, it looks like the box has got extra thick sides and an unduly small space for the pieces, but this is because the opening of the box leads to a much larger hollow inside the box to which all the pieces must fit in.

The P&L in my opinion poses a reasonably fair challenge. Just when I thought I was about to be able to fit every single piece into the box, I find that I can't fit that one last piece; and out comes all the Ps and Ls again. It took me a couple of hours of trying different layout configurations within the small confines of the box before I finally slotted in the last P on top. Overall, a nice and cute little packing puzzle but those with large hands and fingers may find the small pieces a bit fiddly and clumsy to handle.


  1. I found it was easier to solve the puzzle outside of the box. This is pretty easy, but you then discover you can't actually insert the pieces one at a time in the box. So I played around with the configuration, again all outside the box, until I found one combination where the pieces could be inserted one at a time.

  2. George,

    Hmm, maybe I should have tried to solve it first outside the box too!

    What I did was to determine first how the top layer (with its fixed layout) would go over the bottom layer and the location of the spaces required for both layers to mesh nicely. This would then determine how the bottom layer would look like inside the box. Based on this I then tried the different configurations to achieve the correct layout of the bottom layer inside the box....

    A question...is there more than 1 solution to this puzzle??

  3. According to BurrTools the answer is ... yes. It finds three solutions with no constraint on the pieces in the first layer. All three of them have IPP in the top layer (and with the 31 L in the same orientation), so all three are valid solutions. Two of them are almost identical because 2 L's that make a rectangle are simply rotated. This is the one I found. So I would say there are really only two solutions. It surprises me to find there are no solutions which do not have IPP in the top layer!

  4. Hi George

    I see, thanks. Yeah, your last point is rather surprising...

  5. since the pieces are 50 voxels is the inside space 5x7?