# Two similar hand tiling puzzles

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.

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

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

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