T-Puzzle

The T-Puzzle is the classic dissection puzzle with its authentic geometry: four polygonal pieces — one isosceles right triangle, two right trapezoids and an irregular pentagon with a 45-degree notch — that must be arranged to form a capital letter T. Despite having only four pieces, it is famous for being surprisingly difficult: psychologists have studied it as a textbook case of functional fixedness, since most solvers spend their time trying to fill the notch instead of realizing that the notch IS the inner corner of the T.

Rules

1. The target is a capital T: a horizontal bar over a centered vertical stem, all of the same thickness.
2. You are given the four classic pieces: an isosceles right triangle, two right trapezoids of different sizes, and an irregular pentagon.
3. Drag a piece from the tray onto the board, or select it with a tap and drop it where it fits. Pieces snap to the puzzle's lattice; edges and 45-degree cuts must line up.
4. Pieces may be rotated and flipped (each has up to 8 orientations). Tap a placed piece to return it to the tray.
5. To win, all four pieces must sit inside the T without overlapping — since their areas add up to exactly the T's area, that means covering it completely.
6. Difficulty changes the game: Easy shows the solution's cut lines inside the silhouette and grants 5 hints; Medium is the plain upright T with 3 hints; Hard turns the T on its side (rotated 90 or 270 degrees) and starts the pieces in random orientations, with 2 hints; Expert rotates the T in a random direction, also scrambled, with a single hint.

Strategies

• The notch is the corner: the pentagon's 45-degree notch is not a defect to hide — it is the inner corner of the T. The pentagon straddles the junction between bar and stem.
• Don't fill the notch: the most common failure is rotating the pentagon so that another piece fills its notch. That arrangement can never complete the T.
• The big trapezoid can hide in the bar: one trapezoid fits neatly across the top bar — and that tempting placement is a dead end. The stem needs it.
• Flip early: several pieces are chiral in practice once you fix their role; if a placement looks close but wrong, try the mirrored orientation.
• Work from the stem: the stem is one thickness wide and four long; only certain edges of the pieces can form its straight sides.

The T-Puzzle has roots in the broader tradition of dissection puzzles, which date back to ancient Greece. Archimedes is credited with the Stomachion, a 14-piece dissection puzzle from the 3rd century BC, making geometric dissection one of the oldest forms of mathematical recreation.

The modern T-Puzzle became popular in the early 20th century as a promotional giveaway and advertising novelty. Companies would print their logos or messages on the pieces and distribute them as clever marketing items — the recipient would be engaged with the brand while attempting to solve the puzzle. This tradition continues today, with T-Puzzles remaining popular corporate gifts and trade show giveaways.

The classic four pieces — an isosceles right triangle, two right trapezoids and an irregular pentagon — are cut from a square, and the puzzle's trick is that they tile the T in only one essential way. This game uses that authentic geometry: the pieces and the T keep the exact proportions of the traditional wooden puzzle, so the historical difficulty carries over intact.

The puzzle gained mathematical attention through its connection to dissection geometry. The principle that a simple shape can be divided into pieces that are extremely difficult to reassemble illustrates important concepts in combinatorial geometry and spatial reasoning. Henry Dudeney, the famous English puzzle creator active in the early 1900s, popularized many similar dissection puzzles in his books and newspaper columns.

The T-Puzzle's enduring appeal lies in its paradox of simplicity: four pieces and a clear target shape, yet most people cannot solve it without help. Psychologists have studied the T-Puzzle as an example of functional fixedness — the cognitive bias that makes people see objects only in their conventional orientations, preventing them from finding the solution that requires an unexpected flip or rotation.