The figure shows all 6 colorings with for different colors of a $1\times 1$ square divided in four $\tfrac{1}{2} \times \tfrac{1}{2}$ cells (two colorings are considered equal if one is the result of rotating the other). Each of the $1\times 1$ colorings will be used as a piece for a puzzle. The pieces can be rotated but not reflected. Two pieces fit if when sharing a side, the touching $\tfrac{1}{2} \times \tfrac{1}{2}$ cells are the same color respectively (see examples). ¿Is it possible to assemble a $3 \times 2$ puzzle using each of the 6 pieces exactly once and such that every pair of adjacent pieces fit?