These puzzles all involve **polyominoes,** shapes constructed by attaching two or more congruent squares side-by-side.

The shape above is a pentomino because it uses 5 squares, but any number of squares is possible. In the puzzles ahead, you'll fit them together into shapes and patterns like the tesselation below!

The type of puzzle you just did is called a *tiling*. You can assume a tiling will always cover an entire shape and never have any gaps or overlaps.

If one of the squares marked with a letter is removed, the shape on the right can be tiled by the polyomino on the left. Which square should be removed?

For each of the two tetrominoes on the left, it's possible to use 4 copies of that tetromino (with rotation allowed) to tile a 4 by 4 square.

One of the tetrominoes will **not** be able to tile the square. Which one?

If I have the 5 colored shapes shown that I can rotate, and I use each shape once, is it possible to place them so they fit perfectly in a $5 \times 4$ rectangle?

(The checkerboard pattern is a hint!)

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