1. Tiles have greater area than the area of our feet.
2. The weight of the person crossing the slushy patch is exerted over a large area of the tiles.
3. Therefore, there is a decrease in the pressure and hence the tiles do not sink much in the slushy patch of ground. This helps to cross the slushy patch of ground.
[Note: If there were no tiles, the feet will come in direct contact with the slushy ground. The area of the feet being less, the weight of the person will act over a smaller area. Therefore. there will be more pressure and hence the feet will sink into the slushy ground.]