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Bunuel
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M16-05 30 Apr 2026, 10:05
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sharmayogeeta
I did not quite understand the solution. What does the word unique stand for here? say W1, w2, --w5 are 5 white tiles. Then is the pattern w1w2 same or different than pattern w2w1?
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“Unique” means the color pattern matters, not the identity of individual tiles.

So W1W2 and W2W1 are the same pattern because both positions are white in both cases. The white tiles are physically different pieces, but they are identical for the purpose of color arrangement.

The question counts patterns such as white, black, red placements on the 2 by 3 floor, not which specific white tile was used.

For more, check the discussion above and follow the link to the alternative discussion.
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Ditipriya
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M16-05 29 Jun 2026, 03:53
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I like the solution - it’s helpful.
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Bitan2001
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M16-05 09 Sep 2026, 18:28
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The term 'unique' in the question makes it very confusing. I think there will be cases where some patterns are mirror images; should those be removed when counting?
Bunuel

“Unique” means the color pattern matters, not the identity of individual tiles.

So W1W2 and W2W1 are the same pattern because both positions are white in both cases. The white tiles are physically different pieces, but they are identical for the purpose of colour arrangement.

The question counts patterns such as white, black, and red placements on the 2 by 3 floor, not which specific white tile was used.

For more, check the discussion above and follow the link to the alternative discussion.
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Bunuel
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M16-05 09 Sep 2026, 21:57
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Bitan2001
The term 'unique' in the question makes it very confusing. I think there will be cases where some patterns are mirror images; should those be removed when counting?

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No. Mirror-image patterns are counted separately because the six positions on the floor are distinct. Nothing in the question says that rotations or reflections should be treated as the same pattern.

Here, “unique” simply means a different assignment of colors to the six positions. Only the identity of individual tiles of the same color is irrelevant.
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M16-05 22 Sep 2026, 08:16
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I like the solution - it’s helpful.
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