# Tapa

Tapa is an grid shading logic puzzle with clues that may contain multiple numbers. These numbers represent the lengths of runs of shaded cells in a 3x3 around the clues. Additionally, shaded cells must be connected and no two 2x2 square may be fully shaded.

## Background

Tapa was invented by Serkan Yürekli in 2007, initially under the name T-Paint. Later, the name "Tapa" was chosen as a contraction of "Turkish Area Paint".[1]. Over a hundred Tapa variants have been made[2], and a series of contests dedicated to Tapa variants has been held at Logic Masters India.[3]

TO DO

## Strategy

• [3 3] and [1 1 1 1] clues have the property that a cell in range matches the diametrically opposing cell with respect to the clue. [4] clues have the opposite property that a cell in range will always differ from the diametrically opposing cell.
• Other clues that are maximal: [4 2], [5 1], [2 2 1], [3 1 1] have their own properties as well.
• [2 2], [1 1 1], and [5] clues are fully specified if placed on the sides; [1 1] and [3] are fully specified on the corner.
• Clues containing 1's one away from the wall necessarily cannot have the run of 1 sandwiched between the clue and the wall, or else the cell will not have anywhere to escape.
• Small gaps can exclude larger runs. Also you may perform a Nonogram-esque argument - for example if you have a 4 clue in a run of 7, then the central square must be shaded. This is especially useful in the corners and sides, which give a run of 3 and 5 respectively.
• Small numbers often will suggest a connectivity argument. For example, a one-wide corridor, can only pass through with a run of 3+; a two-wide corridor needs at least a run of 3, or two runs of 2.

TO DO