How to Solve Pentomino Puzzles: The 12 Pieces and Tips

By Nesim Razon, independent Android developer

A pentomino puzzle gives you a shape and a handful of pieces, each made of five squares. Your job is to fill the shape completely, with no gaps and no overlaps. Here are the 12 pieces and a way of thinking that makes the puzzles much easier.

Meet the 12 pentominoes

A pentomino is a piece made of five squares joined edge to edge. There are exactly 12 different ones, and they are named after the letters they look like: F, I, L, N, P, T, U, V, W, X, Y and Z. In alphabetical order the set is FILNPTUVWXYZ, which is also the easiest way to remember the full list.

Some are easy to picture. I is a straight line of five. X is a plus sign. T is a T with a long stem. U is a cup, V is a big corner with arms of three, and W is a small staircase. L and Y are long pieces with one extra square (at the end for L, second from the end for Y). N looks like two short lines shifted by one step. P is a 2x2 block with one square sticking out. F and Z are the twisty ones, and F is the hardest to spot at first.

How the pieces move

In Pentolings you play this mode as Fit. Drag a piece from the tray into the shape. As you get close, a ghost shows where it will land, and when you let go it snaps into place. If the spot is not valid, the piece goes back to the tray.

Pieces can be turned and mirrored, so one piece can face the shape in many ways. Tap a piece to rotate it. Press and hold to flip it over like a mirror. If a piece refuses to fit, flip it before you give up on it: the mirrored version is a different position, and it is the most common reason for a piece that looks right but will not go in. In total the 12 pieces have 63 distinct positions on the grid, which is why the same piece can solve so many different shapes.

Where to start: the tight spots first

• Begin at the narrowest or most awkward part of the shape: a corner, a one-square-wide dead end, a thin bridge. Those places have the fewest ways to be filled.
• A dead end that is one square wide can only be filled by the tip of a piece. The long, thin pieces (I, L, Y, N) can reach into it, so look at these first.
• X needs a spot where one cell has all four neighbors free, so it is easy to place or rule out. Do it early.
• I needs a straight line of five free cells. If the shape has only one such line, that is where I belongs.
• If an empty pocket has a size that cannot be reached by whole pieces (for example a closed hole of 1, 2 or 3 cells), you have made a mistake earlier: take that piece back.

Count squares like a chessboard

Here is a trick for harder shapes. Imagine the shape colored like a chessboard. Every pentomino covers either three light and two dark squares or the other way round, with one exception: X covers four of one color and one of the other. So if the shape has a big difference between light and dark squares, X must be part of the answer, and exactly the right side of the board decides where it goes.

You do not have to do this on every level. It is a useful check when you are stuck on a shape with an odd outline, because it tells you early whether your plan can work.

Locked pieces, hints and undo

• Some levels begin with a locked piece already in place. It is marked with a lock, it cannot be moved, and it is part of the final answer. Use it as an anchor and build around it.
• If you place a piece you are not sure about, tap it to send it back to the tray, or drag it to move it. The Undo button takes back your last placements (up to 40 steps) and Restart clears the board after a confirmation.
• Stuck? The Hint button highlights where one piece belongs. You get 3 free hints every day, and when they run out you can watch an optional short ad for 2 more.
• Stars depend on hints: 3 stars with no hints, 2 stars with one or two hints, and 1 star with more. A hint is never a failure, it just costs a star, and you can replay the level.

A worked example: 3x5 with P, U and V

Take a 3x5 rectangle and three pieces: P, U and V. That is 15 squares for 15 squares of pieces, so it should fit. Where do you start? Look at the corners. The V is the only one of the three with a long corner shape, so put it in a corner, with one arm along the left edge and the other along the bottom edge.

Now look at what is left. The U has a notch, a square it does not cover, and that notch must be filled by something. In this puzzle the only piece that can poke a square into the notch is the P, so the U goes on the right edge with its opening facing the middle, and the P slides in with its extra square in the notch. The finished board reads VPPUU, VPPPU and VVVUU from top to bottom. The steps you used are the same as in a hard level: corner first, awkward piece second, the flexible piece last.

Common mistakes

• Forcing a piece that almost fits. If it does not go in after a flip and two or three rotations, it does not belong there.
• Leaving a single square on its own. A lone empty square, or a pocket of two or three, can never be filled, so undo before you go further.
• Saving the corners for last. Corners and dead ends are the first places to settle, not the last.
• Forgetting the lock. A locked piece is part of the answer, so build around it instead of trying to use its space.
• Reaching for a hint at once. A hint only costs a star, but if you look at the shape for one more minute you will often see it yourself, and that is how the pieces become familiar.

A routine that works

First look at the shape and name the awkward spots. Place the pieces that have only one or two possible homes. Then fill the remaining area from the edge inward, leaving the open middle for last, because open space gives you the most freedom to fit the last pieces. If you reach a point where a small gap cannot be filled, back up two or three pieces rather than forcing one.

Pentolings has 150 levels in 15 worlds, starting with tiny three-piece shapes and growing to the full set of 12 pentominoes, so you can learn the pieces gradually.