Can a Chessboard be Tiled with No Overlaps or Half Tiles?

In summary, during an interview for programmers, a puzzle was presented that asked if a domino could tile a chessboard with no overlaps, no overhangs, and no half tiles. The question was whether or not this could be proven, and it was confirmed that this is not a trick question. Two individuals attempted to solve the puzzle at the same time and both came to the same conclusion, possibly suggesting the existence of morphogenetic fields.
  • #1
DaveC426913
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Saw this puzzle during an interview for programmers. Thought it was kind of clever.

Can the domino tile the chessboard with no overlaps, no overhangs and no half tiles?

If so, how can you prove it? If not, how can you prove it?

No, this is not a trick question (or trick answer).
 

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  • #2
DaveC426913 said:
Saw this puzzle during an interview for programmers. Thought it was kind of clever.

Can the domino tile the chessboard with no overlaps, no overhangs and no half tiles?

If so, how can you prove it? If not, how can you prove it?

No, this is not a trick question (or trick answer).

Oh crap, Dave, I have homework due tomorrow, but then you go and put this in front of me...
 
  • #3
Hint: each domino covers one blank and one white square.
 
  • #4
Removed the answer.
 
  • #5
AlephZero said:
Hint: each domino covers one blank and one white square.

Lol. We both were solving it at the same time, and ended at the same conclusion. So there is something to morphogenetic fields after all.
 

1. How many tiles are needed to cover a chess board?

The number of tiles needed to cover a chess board is 64. This is because a chess board has 64 squares in total.

2. Is it possible to cover a chess board with only one type of tile?

No, it is not possible to cover a chess board with only one type of tile. This is because a chess board has both black and white squares, and a single type of tile cannot cover both colors.

3. What is the minimum number of colors needed to cover a chess board without any adjacent tiles being the same color?

The minimum number of colors needed to cover a chess board without any adjacent tiles being the same color is 2. This is because a chess board has alternating black and white squares, and only two colors are needed to achieve this pattern.

4. What is the maximum number of tiles that can be placed on a chess board without overlapping?

The maximum number of tiles that can be placed on a chess board without overlapping is 32. This is because a chess board has 64 squares in total, and each tile covers two squares. Therefore, 32 tiles can be placed without overlapping.

5. Can a chess board be tiled with different shapes of tiles?

Yes, a chess board can be tiled with different shapes of tiles. As long as the tiles can fit together to cover the entire board without overlapping, any shape can be used. However, the most common and traditional shape used for tiling a chess board is the square tile.

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