# Is this more than a packing puzzle?

I bought this set of wooden blocks at a garage sale today, and although it was a challenge to fit them in the box, I suspected they were more than just a packing puzzle. Can you guess what else they are used for?

Hint 1:

There are 32 blocks in total, the exact same shapes in light and dark.

Hint 2:

There are six different shapes, and the shapes have meaning.

• Maybe add a hint saying how many shapes appeared once each, twice each, etc.? – supercat Jul 14 at 16:38
• How about kindling :) – Kent S Jul 15 at 4:58

They are:

A set of abstract chess pieces: the short rectangular prisms are pawns (8 white, 8 black), the L pieces are probably knights (2 white, 2 black), the pentagonal pieces are probably bishops (2 white, 2 black), the marked longer rectangular prisms are probably rooks (2 white, 2 black) - based on general representations as the L pieces can look like a horse head, the pentagonal pieces can look like a bishop's hat, and the squares could look like towers, the longest rectangular prisms are probably kings and the octagons are probably queens (1 white and 1 black, each) based on their movement patterns.

• It is so obvious once it's pointed out, that it makes me wonder why I didn't see it. – Jaap Scherphuis Jul 14 at 9:20
• Excellent answer, @phenomist! I added my own interpretation, and some extra photos in my own answer. – Don Kirkby Jul 15 at 5:47

I had a slightly different interpretation of the shapes' meanings. The rook's edges are marked, because it moves orthogonally. The bishop has diagonal edges, because it moves diagonally, and the knight is L-shaped, because it moves in an L shape.
Here's a photo of the pieces on a chess board:

Finally, here's a photo of all the pieces in the box. The tricky packing isn't visible.

• I don't know what the etiquette is on this site for spoilers in the comments, @MrPie, but perhaps you could edit your comment to "the coolest design of this item I have ever seen." As for your question, I found it at a thrift sale, so I don't know where it was originally bought. I tried googling for similar items, but couldn't find an exact match. – Don Kirkby Jul 15 at 19:10
• Sorry about my spoiling comment; I guess I got carried away since the answer has already been accepted and I quite love this design. Again, my apologies. Comment deleted. (With that being said, perhaps you should not mention the link in the word "googling" hehe.) But no stress if you can't find out where exactly it came from. The similar items looked nearly the same, so I'll probably make it a goal to get that. Thanks, and great puzzle! :) – Mr Pie Jul 15 at 19:16
• Not a big deal, @MrPie, but thanks for cleaning it up. – Don Kirkby Jul 15 at 19:21

The tricky packing interests me.

The height of each part appears to be 1, 2, or 3 units.
This gives a total volume of $$(4 \times 3) + (12 \times 2) + (16 \times 1) = 52$$ units.
But the volume of the box seems to be only $$4 \times 4 \times 3 = 48$$ units.

So how could it be done? My guess:

If the knights are nested in pairs then they take only 6 units instead of 8.
But that still leaves 2 pawns that will not fit.

Now, if the four bishops are placed together, but twisted, a hole is available between them.
That hole will take the remaining 2 pawns, diagonally.

Edit: it turned out that the solution of @JaapScherphuis is better

This saves the needed volume of 4.

• @JaapScherphuis yours seems better - I have added it. – Weather Vane Jul 15 at 15:14
• Yes, @JaapScherphuis, the second diagram is correct. I'm impressed you could solve it just from the photograph. – Don Kirkby Jul 15 at 15:35