Pairs of Pentominoes in Rectangles
The problem of finding rectangles with pairs of pentominoes was first suggested in 1978. A detailed analysis of this problem is given in 'Tiling Rectangles with T and C Pentominoes" by Earl S. Kramer in Journal of Recreational Mathematics Vol. 16(2), 1983-84 and 'Tiling Rectangles with Pairs of Pentominoes" by Earl S. Kramer in Journal of Recreational Mathematics Vol. 16(3), 1983-84 although the data are incomplete. The tables below gives a list of all prime rectangles for various pairs most of the extra data being from Mike Reid. (In these tables the C pentomino cited above is given its more usual U name)
The CT, UV and VW combinations are the most complex but the tables are now complete thanks to Mike Reid's finding of the 29x35 UV rctangle.
The smallest rectangle for each of these pairs is shown below.