# An "XL" puzzle: A different way to design overlapping shape puzzles

Recently I came across an interesting puzzle (Joy of Japanese puzzles). Eight same size square sheets were placed inside a bigger square with their edges showing. See below

One has to show the overlapping order in which they were placed with explanation or drawing (exploded view)

I think this type can be expanded to a catagory of puzzles that use different shapes (rectangle, triangle,polygon etc.)

These can be designed using Excel spreadsheet nicely. Hence I call them "XL" puzzles.

As many of you know, you can "insert" a shape on the sheet using the Task bar commands. If you copy that shape on the same sheet and drag it to partially overlap the orginal shape then the copy shape covers the original shape. Then the next Copy goes over both the original and the first copy and so on. See below

With this technique you can design and build many partially overlapping shapes; simple to complicated. Now you can have "XL" puzzles very similar to the image above.

Here is an example

I have placed seven same size Rectangles in a bigger rectangle. All the area in the bigger rectangle is covered by them. They are either horizontal or vertical only. Rectangle 1 is on very top. All other rectangles are exactly same dimensions as number 1

Establish the order in which they were placed with a drawing

The answer to this puzzle is

So here is a more complicated XL puzzle

Ten rectangles, same size are placed in order inside a bigger rectangle. With a drawing show the order in which they are placed. The rectangle at the bottom left corner is on the top and that is the shape/size of all others. Placement is vertical or horizontal only.

I do not know what Tag to use. Could not find "Shape" Tag!

• Actually, there is a nice simple deterministic solution to solve any XL puzzle here :). Also, your example solution are not unique imo: 4th and 5th can be swapped (if 4 and 5 are not overlapping) cmiiw. Apr 21, 2020 at 14:49

I believe this is the order:

And moving them closer together:

We get the same! (My rectangles are just slightly longer)

Note:

There is a 'gap' in the original image, middle right, where you can see the lines of the excel grid. I'm assuming this is intentional, I've made sure there is a gap in my solution as well.

• Note that rot13(gurfr qba'g "ragveryl pbire" gur erpgnatyr). For the avoidance of doubt, rot13(V qba'g guvax guvf vf n zvfgnxr ba lbhe cneg; V nterr jvgu lbh nobhg gur beqre naq lbh pna frr gur tnc va gur bevtvany vzntr gbb.) Apr 21, 2020 at 13:56
• @GarethMcCaughan I think that might be intentional from DEEM, not sure. I've made sure there's a gap in mine too, but I'll edit that in Apr 21, 2020 at 14:03