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