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".. Over a hundred Tapa variants have been made, and a series of contests dedicated to Tapa variants has been held at Logic Masters India.

Puzzle Application

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.

Notable Examples

TO DO

See Also

• List of Tapa puzzles