11 × 35, 11 × 42, 11 × 49, 11 × 56, 11 × 63

12 × 21, 12 × 28, 12 × 35

14 × 14, 14 × 19, 14 × 20, 14 × 22, 14 × 23,
14 × 24, 14 × 25, 14 × 26, 14 × 27, 14 × 29,
14 × 30, 14 × 31, 14 × 32, 14 × 35

15 × 21, 15 × 28, 15 × 35

16 × 21, 16 × 28, 16 × 35

17 × 21, 17 × 28, 17 × 35

18 × 21, 18 × 28, 18 × 35

19 × 21

20 × 21

21 × 21, 21 × 22, 21 × 23, 21 × 25, 21 × 26

complete

smallest rectangle: 14 × 14

smallest odd rectangle: 15 × 21

Klarner [2, Figure 4] gives the first rectangle, 12 × 21, for this shape, and later [3, Figure 6] gives the minimal rectangle, 14 × 14. Gardner [1, Figure 83, p. 187] also gives the 14 × 14 square, and attributes it to James E. Stuart. The smallest odd rectangle, 15 × 21, was given in [4, Figure 13] and [5, Figure 11]. All the prime rectangles were also found independently by Andrew Clarke.

**References**

[1] Martin Gardner, Polyominoes and Rectification, Chapter 13 in
Mathematical Magic Show, The Mathematical Association of America,
1989.

[2] David A. Klarner,
Some Results
Concerning Polyominoes,
*Fibonacci Quarterly* **3** (1965), no. 1, pp. 9-20.

[3] David A. Klarner,
Packing a
Rectangle with Congruent *N*-ominoes,
*Journal of Combinatorial Theory* **7** (1969) pp. 107-115.

[4] William Rex Marshall,
Packing
Rectangles with Congruent Polyominoes,
*Journal of Combinatorial Theory, Series A* **77** (1997),
no. 2, pp. 181-192.

[5] Michael Reid,
Tiling Rectangles and
Half Strips with Congruent Polyominoes,
*Journal of Combinatorial Theory, Series A* **80** (1997),
no. 1, pp. 106-123.

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Updated August 25, 2011.