Puzzleup 2018 (6) THREE ORDERS - 拼圖

題目網址: http://www.puzzleup.com/2018/
http://www.puzzleup.com/2018/puzzle/?6
答題時限: ９月6日７ＰＭ－比賽結束（約12月12日）
加分時限: ９月6日７ＰＭ－９月12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）　　

◆THREE ORDERS

Three separate arrangements of five basketball players are made by ordering
based on their heights, ages and shirt numbers. In each type of arrangement,
the position of a player is never the same. How many distinct arrangements
are there satisfying this condition?

五位籃球員，分別依身高，年齡，與背號做出三種排序。
每位球員在三種排序中的位置皆不相同。
有多少種組合可以滿足以上情形？

Example: If there were 3 players, the answer would be 12:

1. Height: (A,B,C), Age: (B,C,A), Shirt: (C,A,B)
2. Height: (A,B,C), Age: (C,A,B), Shirt: (B,C,A)
3. Height: (A,C,B), Age: (B,A,C), Shirt: (C,B,A)
4. Height: (A,C,B), Age: (C,B,A), Shirt: (B,A,C)
5. Height: (B,A,C), Age: (A,C,B), Shirt: (C,B,A)
6. Height: (B,A,C), Age: (C,B,A), Shirt: (A,C,B)
7. Height: (B,C,A), Age: (A,B,C), Shirt: (C,A,B)
8. Height: (B,C,A), Age: (C,A,B), Shirt: (A,B,C)
9. Height: (C,A,B), Age: (A,B,C), Shirt: (B,C,A)
10. Height: (C,A,B), Age: (B,C,A), Shirt: (A,B,C)
11. Height: (C,B,A), Age: (A,C,B), Shirt: (B,A,C)
12. Height: (C,B,A), Age: (B,A,C), Shirt: (A,C,B)

例：如果籃球員有三位，答案會是12：

1. 身高: (A,B,C), 年齡: (B,C,A), 背號: (C,A,B)
2. 身高: (A,B,C), 年齡: (C,A,B), 背號: (B,C,A)
3. 身高: (A,C,B), 年齡: (B,A,C), 背號: (C,B,A)
4. 身高: (A,C,B), 年齡: (C,B,A), 背號: (B,A,C)
5. 身高: (B,A,C), 年齡: (A,C,B), 背號: (C,B,A)
6. 身高: (B,A,C), 年齡: (C,B,A), 背號: (A,C,B)
7. 身高: (B,C,A), 年齡: (A,B,C), 背號: (C,A,B)
8. 身高: (B,C,A), 年齡: (C,A,B), 背號: (A,B,C)
9. 身高: (C,A,B), 年齡: (A,B,C), 背號: (B,C,A)
10. 身高: (C,A,B), 年齡: (B,C,A), 背號: (A,B,C)
11. 身高: (C,B,A), 年齡: (A,C,B), 背號: (B,A,C)
12. 身高: (C,B,A), 年齡: (B,A,C), 背號: (A,C,B)

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