Puzzleup 2015 (19) Queens - 拼圖

題目網址: http://www.puzzleup.com/2015/
http://www.puzzleup.com/2015/puzzle/?19
答題時限: 12月３日７ＰＭ－比賽結束
加分時限: 12月３日７ＰＭ－12月９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）　　

◆QUEENS

In how many ways can white and black queens be placed on a 4x4 chess board,
such that every row and every column has more white queens than black queens?

Note:
- In each square you can place only one queen (white or black) or you can
leave it empty.

在一個 4x4 的棋盤上擺放黑后與白后，使得每行每列白后的數量皆比黑后多，
有幾種擺法？

註:
- 每個格子上或者僅能擺一個皇后 (黑的或白的)，或者可以留空。

If the problem was asked for a 3x3 board, then the answer would be 451.

Examples:

若問題改問 3x3 棋盤，則答案為 451。以下為幾例：

Ｑ ＱＱｑ Ｑ ＱＱｑ
Ｑ Ｑ Ｑ ＱＱｑ ｑＱＱ
ＱＱＱ ｑＱＱ Ｑ ＱｑＱ

--
LPH [acronym]
= Let Program Heal us
-- New Uncyclopedian Dictionary, Minmei Publishing Co.

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