# Tiling a rectangle with an odd number of Y pentomoes

Follow-on from Tiling a rectangle with just the Y pentomino

Two questions:

• Find the smallest rectangle that can be tiled with an odd number of Y pentominoes, or prove it impossible

• Find the smallest rectangle that can be tiled with an odd number of just 'right-handed' Y pentominoes, i.e. no 'flipping', or prove it impossible

Here is a 5x10 tiled with right-handed Y pentominoes, by way of illustration. All that prevents it from being a valid answer to both questions, is the fact that there is an even number of them.

• Need the solutions be proven smallest? This sounds difficult with no-computers. Commented May 23, 2018 at 21:48
• @noedne smallest proof not required, smallest will probably be easiest anyway... Commented May 24, 2018 at 0:33
• One observation for the 2nd question: both sides of the rectangle must be odd (obviously) but also divisible by 5 (otherwise, gaps will emerge close to the border). Commented May 25, 2018 at 10:58
• I've stopped searching for a solution to part 2. In fact I believe I have a fairly simple parity/square-numbering impossibility proof if anyone wants to have a go at getting that. I'll post it in a day or two. Commented May 30, 2018 at 8:55
• ...It still eludes me... not as close as I thought. Commented Jun 1, 2018 at 0:30