题目247：双曲线下的正方形
Squares under a hyperbolaConsider the region constrained by 1 ≤ x and 0 ≤ y ≤ 1/x.
Let S1 be the largest square that can fit under the curve.
Let S2 be the largest square that fits in the remaining area, and so on.
Let the index of Sn be the pair (left, below) indicating the number of squares to the left of Sn and the number of squares below Sn.
The diagram shows some such squares labelled by number.
S2 has one square to its left and none below, so the index of S2 is (1,0).
It can be seen that the index of S32 is (1,1) as is the index of S50.
50 is the largest n for which the index of Sn is (1,1).
What is the largest n for which the index of Sn is (3,3)?
题目：
考虑由 1 ≤ x 和 0 ≤ y ≤ 1/x 约束的区域。
设 S1 为曲线下能容下的最大正方形。
设 S2 为剩下区域能容下的最大正方形,以此类推。
设 Sn 对应的二元组 （左边，下面）表示 Sn 左边的正方形和 Sn下面的正方形。
圆形显示了一些由数字标记的正方形。
S2 有一个正方形在其左边，没有方块在其下面，由此 S2 对应的二元组为 (1,0)。
不难得到 S32 对应的二元组为 (1,1) ，与 S50 对应的二元组相同。
50 为使 Sn 对应二元组为 (1,1) 的最大整数 n。
使得 Sn 对应二元组为 (3,3) 的最大整数 n 是多少？
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