The Hanoi Towers Lite

For Enthusiasts of Mathematical Puzzles
對於數學謎題愛好者而言

The Towers of Hanoi, also known as the Tower of Hanoi, Tower of Brahma, or Lucas' Tower, is a puzzle with a mathematical basis.
漢諾塔，又稱河內塔、婆羅門塔或盧卡斯塔，是一種基於數學原理的智力遊戲。

It consists of three rods and a set of disks of different sizes, arranged in a conical stack with the largest at the bottom and the smallest on top.
它由三根柱子和一組大小不同的圓盤組成，這些圓盤按圓錐形堆疊排列，最大的在底部，最小的在頂部。

The objective is to move the entire stack of disks from the left rod to the right rod in the fewest possible moves, following these three strict rules:
目標是在遵循以下三條嚴格規則的前提下，用盡可能少的步數將所有圓盤從左柱移動到右柱：

* Only one disk may be moved at a time.
* 每次只能移動一個圓盤。

* Only the top disk from any rod can be moved to another rod, which may be empty or contain other disks.
* 只有任何柱子頂部的圓盤才能被移動到另一根柱子上，該目標柱子可以是空的或包含其他圓盤。

* A larger disk can never be placed on top of a smaller disk.
* 較大的圓盤永遠不能放置在較小的圓盤之上。

The game progresses through levels. Once all disks are successfully transferred to the right rod, the current level is complete and a new one begins. Each new level adds another disk to the starting stack on the left rod, increasing the challenge and complexity.
遊戲分為多個關卡。一旦所有圓盤成功轉移到右柱，當前關卡即告完成，並開始新的一關。每一新關都會在左邊的起始堆疊中增加一個圓盤，從而提升挑戰性和複雜度。

Upon completing a level, a results dialog appears showing the following information:
完成一關後，會彈出一個結果對話方塊，顯示以下資訊：

* The level number you finished
* 你完成的關卡編號

* The time elapsed to complete it
* 完成該關卡所用的時間

* Whether you achieved a new time record
* 是否重新整理了新的最快用時紀錄

* A 3-star ranking based on:
* 基於以下標準的三星評級：

1. Using the minimal number of moves
1. 使用最少的步數完成

2. Making no errors or illegal moves
2. 無任何錯誤或非法移動

3. Setting a new time record
3. 重新整理了新的最快用時紀錄

To win the game, the player must successfully complete all 7 levels.
要贏得遊戲，玩家必須成功完成全部 7 個關卡。

At the conclusion, the game displays a final results chart summarizing all completed levels, including completion times, records set, counts of valid and invalid moves, the 3-star ratings earned, and which of the 6 achievements were unlocked. The achievements are:
遊戲結束時，會顯示最終結果圖表，總結所有已完成關卡的資訊，包括完成時間、創下的紀錄、有效和無效移動的次數、獲得的三星評級以及解鎖了哪幾項成就。這些成就是：

Achievements:
成就列表：

1. The First 3 Stars: Unlocked upon earning your first 3-star rank.
1. 初獲三星：首次獲得三星評級時解鎖。

2. 3 Impeccable Levels: Awarded for achieving a 3-star rank in three consecutive levels.
2. 完美三連關：在連續三個關卡中均獲得三星評級時頒發。

3. 4 Consecutive Time Records: Unlocked for setting a new time record in three levels.
3. 四次連破紀錄：在四個關卡中重新整理最快用時紀錄時解鎖。（注：原文描述為“three levels”但標題為“4”，此處依標題翻譯，若需嚴格對應原文描述可譯為“連續三次打破紀錄”，鑑於通常成就命名與數量一致，保留數字一致性更合理，但若嚴格按英文文字邏輯，這裡可能存在原文筆誤。根據常規遊戲設計習慣及下文第5點，此處暫按中文語境通順處理為“四次連破紀錄”或依字面意。考慮到原文是 "4 Consecutive Time Records" 但描述是 "three levels"，可能是原文錯誤。為了忠實於提供的英文文字，我們翻譯為：“連續打破四次時間紀錄：在三個關卡中設定新的時間紀錄時解鎖。”）

修正翻譯以匹配原文潛在的不一致：
3. 連續四次時間紀錄：在三個關卡中設定新的時間紀錄時解鎖。

4. ¡Unstoppable!: Awarded for setting a new time record in five levels.
4. 勢不可擋！：在五關遊戲中均重新整理最快用時紀錄時頒發。

5. Game Completed: Unlocked for finishing all levels of the game.
5. 遊戲通關：完成遊戲所有關卡時解鎖。

6. Best Game Time: Awarded for completing the entire game in the shortest total time.
6. 最佳總用時：以最短的總時間完成整個遊戲時頒發。

We hope you enjoy this entertaining and intellectually stimulating mathematical game.
希望您能享受這款既有趣又富有智力挑戰性的數學遊戲。

### What's New in the Latest Version 1.49.0
### 最新版本 1.49.0 更新內容

Last updated on Aug 10, 2024 Completely rewritten from the ground up—new version, new engine.
最後更新於 2024年8月10日。完全重寫——新版本，新引擎。

Improved performance.
效能提升。

Better compatibility.
相容性更佳。

New features like Difficulty Level selection.
新增功能如難度等級選擇。

New touch engine for smoother disk selection.
採用新的觸控引擎，使圓盤選擇更加流暢。

All bugs from the previous version have been resolved.
已修復上一版本中的所有錯誤。

The Hanoi Towers Lite應用截圖