本論文研究為使用三個杆子對圓盤進行排序的問題。在此問題中，輸入為置於第一個 杆子上的 n 個不同編號的圓盤，而它們的編號從上至下恰為兩個單調序列。我們的目標 為利用三個杆子對圓盤進行移動(一次移動可將任意杆上置頂的圓盤移到任意杆上，並 成為後者上置頂的)，使最終能把所有圓盤「依序」放置在第一個杆子上，其編號從上 至下為單一遞增的單調序列。
本論文中對輸入的不同情況作分類，並提出相對應最少移動步數的「精確緊界」。 其中我們給出一個在一定步數中完成目標的演算法來給定上界;而對於下界，我們給 出一個基於鴿籠原理的證明來證明沒有任何演算法能在少於該步數的方式內完成目 標。

This thesis studies the problem of sorting discs with three pegs. The input contains n discs, which are placed on the first peg; furthermore, the discs have distinct labels from {1, 2, . . . , n}, and when reading from top to bottom, the labels form two monotone sequences. Our goal is to use three pegs to move the disc around (each step takes the top disc from some peg, and move it to become the top disc of another peg), so that in the end, all the discs are sorted on the first peg, with the labels from top to bottom forming a monotone increasing sequence.
The thesis classifies the input into different cases, and for each case, shows an exact bound on the minimum number of steps to achieve the desired output. Here, the upper bound is obtained by designing an algorithm that sorts the input within a certain number d of steps. As for the lower bound, we utilize the pigeonhole principle and shows that no algorithm exists whose number of steps is less than d.

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