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Problem 173

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Using up to one million tiles how many different “hollow” square laminae can be formed?

We shall define a square lamina to be a square outline with a square “hole” so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae:

With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.

Using up to one million tiles how many different square laminae can be formed?

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使用最多一百万块地砖能拼出多少种不同的“空心”方形基板？

我们定义一个方形基板为一个拥有方形外框，中间有一个方形的“洞”且在水平和竖直方向上均对称的图形。例如，使用恰好32块方形地砖，我们可以拼成两种不同的方形基板：

使用最多一百块地砖，我们能够拼出41种不同的方形基板。

使用最多一百万块地砖，能够拼出多少种不同的方形基板？

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