A tile is a square with a color on each side, taken from a finite set C = {c1, . . . , ck} of colors. Let T be a set of tiles. A tiling of a discrete n n square with T is a way to put n 2 tiles, each taken from T into each of the positions in the square (possibly reusing the same tile many times in the square), so that every pair of adjacent tiles has a matching color on the side where they touch. Show that Tiling = {hT, 0 n i | the n n square has a tiling with T} is contained in NP.

1. A tile is a square with a color on each side, taken from a finite set -e,.. . ,%) of colors. Let T be a set of tiles. A tiling of a discrete n x n square with T is a way to put n2 tiles, each taken from T into each of the positions in the square (possibly reusing the same tile many times in the square), so that every pair of adjacent tiles has a matching color on the side where they touch. Show that TILING-{T, 0n l the n n square has a tiling with is contained in NP. 1. A tile is a square with a color on each side, taken from a finite set -e,.. . ,%) of colors. Let T be a set of tiles. A tiling of a discrete n x n square with T is a way to put n2 tiles, each taken from T into each of the positions in the square (possibly reusing the same tile many times in the square), so that every pair of adjacent tiles has a matching color on the side where they touch. Show that TILING-{T, 0n l the n n square has a tiling with is contained in NP