Perimeter of tile shapes

In your book, Maths Mela (Chapter 11), there is a game for two players, played with square tiles and a die. Each tile has sides of 1 unit. You roll the die, take that many tiles and arrange them into a shape, with whole sides touching. Then you find the perimeter of the shape by counting the tile edges on the outside. The next player rolls and adds tiles to the same shape, without moving the tiles already there. The first player to make the perimeter 24 wins.

In the book, the first player rolls a 4. She puts 3 tiles in a row and 1 tile under the left end, making an L shape. Counting the outside edges: 3 along the top, 1 at the right end, 2 along the bottom of the row, 1 on the right of the hanging tile, 1 under it, and 2 up the left side. That is 3 + 1 + 2 + 1 + 1 + 2 = 10. Edges where two tiles touch are inside the shape, so they do not count.

Then a fifth tile is put on top of the middle tile of the row. It covers 1 edge that was on the outside, but adds 3 new outside edges. So the perimeter goes from 10 to 12. Adding a tile that touches the shape along just one side always adds 2 to the perimeter.

But a tile that fits into a corner, touching the shape along two sides, covers 2 outside edges and adds 2 new ones, so the perimeter stays the same. Three tiles in an L have a perimeter of 8; fill the corner and you get a 2 by 2 square, whose perimeter is still 8.