How Can You Tile an $8 \times 8$ Chessboard with L-Shaped Pieces?

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  • #1
Ackbach
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Here is this week's POTW:

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Tile an $8 \times 8$ chessboard, with one square missing, with L-shaped pieces that cover three squares each. The missing square is arbitrary.

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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
 
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  • #2
No one solved this week's POTW. Here is my solution below:
You sort of recursively move outward from the missing square, as shown:

View attachment 4664

Note I haven't completely covered the $8\times 8$ square, but you should be able to see the pattern, and how you could complete it.
 

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Related to How Can You Tile an $8 \times 8$ Chessboard with L-Shaped Pieces?

1. How many L-shaped pieces are needed to tile an 8x8 chessboard?

The minimum number of L-shaped pieces needed to tile an 8x8 chessboard is 32.

2. Can the L-shaped pieces be rotated or flipped?

No, the L-shaped pieces cannot be rotated or flipped. They must be placed in the same orientation as they are shown on the chessboard.

3. Are there any specific rules for placing the L-shaped pieces on the chessboard?

Yes, the L-shaped pieces must be placed in a way that they cover exactly three squares on the chessboard without overlapping or leaving any gaps.

4. Is it possible to tile the chessboard with only one type of L-shaped piece?

No, it is not possible to tile the chessboard with only one type of L-shaped piece. A combination of two different types of L-shaped pieces is needed.

5. Can the chessboard be tiled with different combinations of L-shaped pieces?

Yes, there are multiple combinations of L-shaped pieces that can be used to tile the chessboard. However, all combinations will require a total of 32 L-shaped pieces.

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