# Tiling rectangles with a Heptomino plus 2x2 square

Previous puzzle in this series Tiling rectangles with Heptomino plus rectangle #7

The goal is to tile rectangles as small as possible with each of the given heptominoes (see diagram in example below) plus 2x2 squares.

Example Using the snake heptomino 'e' plus 2x2 squares you can tile a $3\times 5$ as follows: Use each of these heptominoes. Solutions may exist for other heptominoes, I only found solutions for these ones. Note that I omitted labels 'W', 'j', 'l': All of these could all be tiled by hand, of course the bigger ones will be challenging. I'm making this one a 'hand tiling only' puzzle. In other words, use a computer to do anything except look up or compute the arrangements.

• There are trivial solutions for 'j' and 'l' - put two 'j's together to make a 2x7 rectangle. If a 2x2 is required, stick it on the end to make a 2x9. Likewise, two 'l's make a 2x7 and you can add a 2x2 on the end. Or if the 2x2 is not required, one 'l' by itself makes a rectangle already. 'W' may be impossible. – Darrel Hoffman Oct 17 '19 at 14:22
• j and I were omitted because they trivially make rectangles on their own. W is probably impossible, I haven't thought of an elegant way to stop my program bogging down making width-7 right-angles when tiling the quarter plane. – theonetruepath Oct 18 '19 at 1:14

• @theonetruepath Glorfindel has found improvements for B,D,G, so I've been trying to find better solutions for H,I,J, but not getting very far. They all have $7\times16$ solutions, but that is the same area as the $8\times14$ I already found. – Jaap Scherphuis Jun 30 '18 at 5:24