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 T pentomino plus rectangles
Tiling rectangles with U 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 V pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one V-pentomino will tile. Examples shown, with the $1\times 1$, $1\times 2$ or $2\times 2$, you can tile a $3\times 3$ as follows:
Now we don't need to consider $1\times 1$, $1\times 2$, or $2\times 2$ any longer as we have found the smallest rectangle tilable with copies of V plus copies of each of those three.
There are at least 20 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.
Answer
Here are (most of) the remaining ones. An easy one for 1x5:
and a more difficult one for 1x6:
1x7 takes a lot more:
24x11 = 264
1x8:
16x11 = 176
1x9:
1x10:
13x30 = 390
1x12:
14x42 = 588
2x3:
4x8 = 32
2x5:
5x6 = 30
2x6:
8x12 = 96
2x7:
16x19 = 304
2x8:
17x18 = 306
2x9:
21x24 = 504
3x4:
3x5:
11x35 = 385
3x7:
13x48 = 624
3x8:
33x38 = 1254
4x5:
21x40 = 840
4x6:
5x6:
38x60 = 2280
I assume the number of solutions here is infinite (probably in both directions), I'll post more when I have them.
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