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

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  • #1
Ackbach
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MHB
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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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FAQ: How Can You Tile an $8 \times 8$ Chessboard with L-Shaped Pieces?

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.

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.

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.

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.

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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