Puzzleup 2018 (20) CODE SETS - 拼圖

題目網址: http://www.puzzleup.com/2018/
http://www.puzzleup.com/2018/puzzle/?19
答題時限: １２月13日７ＰＭ－比賽結束（約12月19日）
加分時限: １２月13日７ＰＭ－１２月19日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆CODE SETS

You will create code sets using A, B, C, D, E, F letters.

‧ A set contains at least two codes.
‧ Each letter is used exactly once by the code set.
‧ Each code contains at least two letters.
‧ When the order of codes in the set changes, it is still considered
the same code set.
‧ When the order of letters in a code changes, the code set is
considered different.

How many different code sets can be created?

If the question were asked for A,B,C,D letters, the answer would be 12.

(AB, CD), (AB, DC), (AC, BD),
(AC, DB), (AD, BC), (AD, CB),
(BA, CD), (BA, DC), (CA, BD),
(CA, DB), (DA, BC), (DA, CB).

你要用A,B,C,D,E,F等字母造出編碼組合。

．每個組合至少包含兩段編碼。
．每個字母都會在編碼組合中出現剛好一次。
．每段編碼至少包含兩個字母。
．組合中的編碼次序改變時，視為相同組合。
．編碼中的字母次序改變時，視為不同編碼。

問能造出多少種不同的編碼組合？

如果問題只有A,B,C,D四個字母的話，答案會是12。

(AB, CD), (AB, DC), (AC, BD),
(AC, DB), (AD, BC), (AD, CB),
(BA, CD), (BA, DC), (CA, BD),
(CA, DB), (DA, BC), (DA, CB).

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