Inspired by Polyomino Z pentomino and rectangle packing into rectangle
Also in this series: Tiling rectangles with F pentomino plus rectangles
Tiling rectangles with N pentomino plus rectangles
Tiling rectangles with U pentomino plus rectangles
Tiling rectangles with V pentomino plus rectangles
Tiling rectangles with W pentomino plus rectangles
Tiling rectangles with X pentomino plus rectangles
The goal is to tile rectangles as small as possible with the T pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle a×b, find the smallest area larger rectangle that copies of a×b plus at least one T-pentomino will tile. Examples shown, with the 1×1 or the 1×2, you can tile a 3×3 as follows:
Now we don't need to consider 1×1 or 1×2 any longer as we have found the smallest rectangle tilable with copies of T plus copies of 1×1 and 1×2.
There are at least 10 more solutions. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging.
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