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

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    Board Chess Puzzle
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Discussion Overview

The discussion revolves around the puzzle of whether a chessboard can be tiled with dominoes without overlaps, overhangs, or half tiles. Participants explore the implications of this problem, including potential proofs for both affirmative and negative answers.

Discussion Character

  • Exploratory, Debate/contested, Homework-related

Main Points Raised

  • One participant presents the puzzle as a clever challenge, inviting others to consider the conditions for tiling a chessboard with dominoes.
  • Another participant expresses urgency due to an impending homework deadline, indicating a personal stake in the discussion.
  • A later reply humorously notes a simultaneous conclusion reached by two participants, suggesting a shared understanding or insight into the problem.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants have not explicitly agreed on whether the chessboard can be tiled or on the methods of proof.

Contextual Notes

The discussion lacks detailed mathematical steps or definitions that could clarify the assumptions underlying the tiling problem.

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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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...
 
Hint: each domino covers one blank and one white square.
 
Removed the answer.
 
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.
 

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