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I'm stuck with the following question which is taken from SAT-like exam:

How many $ 5 \times 5 $ ceramic tiles are needed to cover rectangular area whose size is $ 10^4 $ units squared (you can't cut the tiles).

The answer that I've got is $400$ (${10^4} \over {5*5}$), however, it is wrong. I don't understand where's the problem. I would appreciate any help.

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    @AndréNicolas Well, it could be. However there is no such answer as "depends on shape", so it could be that the question is poorly-worded or there is some mistake in the book. Anyway, thank you for your suggestions.2012-12-12

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If you mean you got $400$ by dividing $10^4$ by $5*5$ it looks good to me. The only problem I see is if the question meant $(10^4$ units$)^2$, but using "rectangular" seems to suggest it was $10^4$ units$^2$

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    My point on $(10^4$ units$)^2$ was that it could represent a square $10^4$ on a side, when you would need many more squares. But I agree with you that the answer should be $400$2012-12-12
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It depends. If the sides of the ractangle are divisible by $5$, then $400$ will suffice. If the rectangle is $1\times 10000$, you need $2000$ tiles (well, I could get along with about $1500$, but those won't be parallel to the axis). If the rectangle is $0.001\times 1000000$, the number gets even bigger. Thusthe correct answer in my opionion would have been "It depends on the exact shape of the rectangle". Which is not among 400, 500, 600, so it's indded "none of them".

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    The hint that you cannot cut tiles should give it away: As soon as the shape of the rectangle would *require* you to cut tiles for a wasteless cover, you know that a cover without cutting is wasteful, hence may require more tiles than the mere quotient of areas suggests.2012-12-12