Interesting series: Board coverage

There are often many examples in mathematics: A complicated mathematical problem is proved by a very delicate and concise method. These proofs often reflect the subtlety of mathematics, which is incredibly impressive.

Let's look at a classic example: if there is an 8*8 chessboard, two grids are removed. Can I use 31 1*2 dominoes to cover the entire board.

I believe many people know the result. The reason is clear: we have colored the entire board with red and white. We just need to put a 1*2 card on the board. It will inevitably cover one red, one white, and two grids, but this figure has 32 red grids and 30 white grids, so we cannot cover the entire board in any way.

Some people have to ask: what is the result if one grid is removed from the 1 red and 1 white grids? You can try it by yourself. Can you prove it can be covered? Or can we provide an inverse example?

It is said that when the problem came out, it was finally proved through complicated theories. That is, as long as a red, white, and two cells are removed from this graph, they will certainly be overwritten.
Here, we will see how to prove a complicated problem through a simple method. Next we will not only prove that the data can be overwritten, but also provide the method of overwriting. Here you may think of the constructor. If a group of solutions are constructed, the original problem is solved.
We cut out the original checkerboard as shown in the following way: (along the Yellow Line and Green Line)

We turn this board into a ring. Note that the entire ring is black and white. Let us remove a red lattice and a white one. We will get two chains: each chain is red-> White-> Red...-> White. In this way, we only need to place the two grids along the chain (note that the two grids connected do not exist in a different shape than the bone card: 1*2. Can you find the second shape ?). After the two chains are completed, the Board will be fully covered and our problem will be solved.

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