# Tile-laying for beginners

Coldport is celebrating having a new town hall by laying a tiled design in the public square in front of the building. The design is also square: $$5\times 5$$ tiles square, in fact, and features three interlocking paths in three colours. The coloured squares around the edges of the grid indicate where the paths enter and exit, but the original design layout has been lost somewhere between the town hall and the Tilelayer's Arms public house. Ensuring that paths do not change colour, lay the tiles out so that:

• all tiles are used
• no path changes colour or breaks
• the entry and exit points are respected.

Tiles 16 and 19 both feature a path crossing itself; the crossing is marked clearly and each leg of the path moves in a straight line and may not turn a corner at the crossing.

Tiles are numbered so answers may be given as a grid such as $$\begin{eqnarray} 1 & 2 \\ 3 & 4 \end{eqnarray}$$ if you prefer. Along with the final solution, solvers should indicate a specific numeric feature of the final grid.

Grid: Tiles: