[jjakkswk] Squared squares

A collection of the smallest squared squares and rectangles. All these results from Stuart Anderson.

Simple Perfect Squared Square: side 112, 21 pieces. Bouwkamp Code (50, 35, 27) (8, 19) (15, 17, 11) (6, 24) (29, 25, 9,2) (7, 18) (16) (42) (4, 37) (33).

Simple Imperfect Squared Square: side 23, 13 pieces. Code (12 11) (2 5 4) (11 1) (3) (1 3) (7 2) (5).

Simple Perfect Squared Rectangle: sides 33 by 32, 9 pieces. Code (18 15) (7 8) (14 4) (10 1) (9). The next smallest one (by perimeter) is 57 by 55 (10 pieces), a considerable gap.

Simple Imperfect Squared Rectangle: sides 15 by 11, 9 pieces. Code (6 4 5) (3 1) (6) (5 1) (4).

Simple Perfect Squared Rectangle, minimizing the ratio of largest to smallest square: sides 7526 by 5620, 23 pieces. Ratio is 2182/576 = 3.79. Code (2182 2096 1336 1912) (760 576) (939 1549) (863 1238 755) (1405 777) (1084 610) (628 1012) (637 601) (2159) (2033) (1685) (1649). [Transcribed by hand from image.]

Simple Perfect Squared Square, minimizing the ratio of largest to smallest square: side 35712, 43 pieces. Ratio is 10558/1312 = 8.05. Code begins (9226 8290 5796 4414 7446) ... and I'm too lazy to transcribe the rest. Another the same size, order, and ratio begins (9455 7793 10478 7446)... I don't know how Google seems to have extracted the code from the PDF file in its snippet (searching for those beginning integer sequences).

I don't know about SISS or SISR which try to avoid squares of wildly different sizes.

Mrs. Perkins's Quilts have many solutions, of which I select the one in which the side length equals the order: side 11, 11 pieces. Code (5 3 3) (2 4) (3 2 2) (4 4) (3). The ratio between largest and smallest square is 2.5, which is pretty good.

These might be good for easy-to-manufacture puzzles.