4
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Make a square from each of these lists of aspect ratio $1:2$ rectangles

  • 1, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17

  • 1, 2, 3, 5, 6, 8, 11, 12, 13, 14, 17, 20

Both tilings are unique. '$1$' means $1\times2$ and '$4$' means $4\times8$ etc... No overlaps/gaps of course.

Trivial by computer, fairly tough by hand. Logic will speed you up.

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The 52x52 image here (given first at 1 pixel per square, then at 4x size) is a solution to the first one. Colours are as follows:

1 white
4 grey
5 mid-blue
6 dark grey
7 light green
9 purple
11 cyan
12 brown/maroon
13 pink
14 green
15 dark blue
17 red

enter image description here enter image description here

And the second (54x54):

1 white
2 black
3 yellow
5 dark grey
6 pink
8 light green
11 light grey
12 purple
13 dark green
14 dark blue
17 cyan
20 red

enter image description here enter image description here

(I haven't any clever techniques to share. I just fitted things in where they seemed to fit neatly, starting with the largest tiles.)

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