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This will test you, a computer will definitely help. Just one set of $1:2$ aspect ratio rectangles this time, but $15$ of them. Short side only is listed. The challenge is to arrange them into a square with no gaps or overlaps. There are several sets of sub-rectangles which can be rotated/flipped to give eight tilings.

1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 25

I tagged it both computer-puzzle and no-computer because I'm pretty sure there are people out there who could hand-tile this.

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  • $\begingroup$ Why use both tags? Removing them implies the same thing. $\endgroup$
    – Rick
    Commented Jan 18, 2018 at 12:59
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    $\begingroup$ Not really... adding a computer tag to a riddle would make no sense and adding no-computer to a riddle would be superfluous. But adding both to this puzzle has meaning. If you are following computer puzzles you would want to see this, just as you might want to see it if you are into hand tiling puzzles. $\endgroup$
    – theonetruepath
    Commented Jan 18, 2018 at 14:16

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A solution is as follows:

enter image description here
Simple area calculations say that we should tile a square with side length 68. I was able to intuitively place the first four rectangles, which made PolySolver's job much easier. As stated in the question, there exist ambiguities in the highlighted red rectangle in the SW corner.

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  • $\begingroup$ Yup that's it. My pic added for completeness. $\endgroup$
    – theonetruepath
    Commented May 22, 2018 at 4:59
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For completeness, the pic in my 'style'. Just the short sides listed:

68_68_15

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