Tapa

Rules and Tips for standard puzzle types, and their variants
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pinkagape
Posts: 107
Joined: Mon 30 Apr, 2012 4:11 pm

Tapa

Post by pinkagape » Thu 15 Oct, 2020 8:24 pm

The puzzle type for the November Division D round is Tapa.

GM Puzzles describes the puzzle rules for Tapa as follows:

Shade some empty cells black to create a single connected wall. Numbers in a cell indicate the length of consecutive shaded blocks in the neighboring cells. If there is more than one number in a cell, then there must be at least one white (unshaded) cell between the black cell groups. Cells with numbers cannot be shaded, and the shaded cells cannot form a 2×2 square anywhere in the grid.

Here is a worked example (though I haven't got any cells with more than one number in this example).

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Cells in the centre of the grid have eight neighbouring cells, and can be harder to see where to start. Cells in the corners or edges have 3 or 5 neighbours and can be better starting points.

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This 3 in the corner only has three neighbours, so they must all be shaded.

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This 4 at the bottom has five neighbours, so whichever four are shaded, the middle three must be shaded.

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Now we have information about the 3 in the centre. two of its neighbours are shaded now, so the four crossed cells cannot be shaded, or there would end up being more than three consecutive shaded cells.

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The 1 on the top now only has two possible cells to shade. It can't shade the one right in the corner, because it wouldn't be able to be part of a single connected wall, so we shade the red square as the only remaining option.

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The red square must also be shaded, or else the top section of wall and the bottom section of wall cannot be connected.

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The two cells with red crosses cannot be shaded or there would be a shaded 2x2 square, which is not allowed.

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We finish the puzzle by completing both lines of 3, for the 3 in the centre and 3 in the bottom right, as they have an x on one side of the shaded line, so we know which direction it must go in. Counting the 2 and the 4 as also finished, we know that no more cells can be shaded in.

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