How to play Shape Fit

Shape Fit is a packing puzzle: a rectangular board must be filled completely with a set of loose pieces. It trains spatial reasoning: turning and mirroring shapes in your head.

The rules

• Cover every square of the board. No gaps are allowed and pieces may not overlap or stick out over the edge.
• Each piece is a polyomino: three, four or five squares joined edge to edge. Within one puzzle every shape appears at most once.
• Some pieces are already fixed on the board. They cannot be moved and they reduce the puzzle to only one or a few ways to finish.
• Loose pieces may be rotated and flipped (mirrored) as often as you like.
• The puzzle is solved as soon as the last piece is placed.

Getting started

Drag a piece from the tray onto the board. A green outline shows where it will land; red means it does not fit. Tap a piece in the tray to select it and tap it again to rotate it, or use the Rotate and Flip buttons. While dragging you can press R to rotate and F to flip. To take a placed piece back, tap it on the board.

A good first move is to look at the empty region next to the fixed pieces. Say the fixed pieces leave a narrow pocket in the top-left corner: row 1, columns 1 to 3, plus row 2, column 1. That is four squares in an L shape, closed off on all sides, so only the L-shaped piece of four can fill it. When a corner is more open, ask which loose pieces can cover row 1, column 1 at all. Usually only two or three can, and trying each in your head shows which leaves a fillable region.

Strategies and tips

• Fill corners and edges first. Corner squares can be covered by few pieces in few orientations, so settling them early removes the most uncertainty.
• Watch for dead pockets. Never leave an enclosed gap of one or two squares: the smallest piece covers three.
• Place awkward pieces early. Shapes such as the X (a plus sign), the W (a staircase) and the long straight five are hard to fit late in the game, when space is broken up.
• Save flexible pieces for the end. Small pieces of three or four squares and the compact P shape adapt to many gaps.
• Count squares. An enclosed pocket of eight squares needs a five and a three, or two fours. That alone can rule out most of the tray.
• Remember the mirror image. Many shapes look different when flipped. If a piece almost fits, flip it.
• Undo cheaply. The Reset button returns all the pieces you placed to the tray but keeps the fixed ones, so you can start a fresh line of thought without losing the puzzle.

How the difficulty is chosen

Shape Fit does not change its difficulty automatically; you pick one of five levels with the buttons above the board, and your choice is remembered. Starter, Easy and Medium use a board of 5×11 squares, with 4, 6 and 8 loose pieces. Hard uses a 6×11 board with 10 loose pieces, and Expert a 7×11 board with 12. Each puzzle is built from a random complete tiling of the board, with pieces released into the tray only while at most three ways remain to fill their space. More loose pieces mean a larger open area and more decisions.

When a level starts to feel easy, move up. The brain seems to benefit most when the challenge rises along with your skill, so a puzzle that keeps stretching you is better training than one you can finish on autopilot. You can read more about what research says about puzzles and brain health.

A short history of shape puzzles

Packing and dissection puzzles have a long history; the Chinese tangram, a set of seven flat pieces that became popular in the early nineteenth century, is a famous example. The family of shapes used here received its name from the American mathematician Solomon Golomb, who introduced the term polyomino in the 1950s and later wrote a book about them. His work, popularised by Martin Gardner’s mathematical games columns in Scientific American, made the twelve pentominoes (the twelve distinct shapes of five squares) a favourite of puzzle fans. A classic challenge is to pack all twelve into a 6×10 rectangle, which can be done in more than two thousand ways. Tetrominoes, the four-square shapes, became world famous through the video game Tetris, created by Alexey Pajitnov in the Soviet Union in the 1980s.

Frequently asked questions