Problem H
Powerful Magic Squares
Input: Standard Input
Output: Standard Output
Time Limit: 4 Seconds
You may already know magic
squares. Here we introduce a more powerful one. Suppose we have a 5x5 square
filled with numbers from 1 to 25, every number appear EXACTLY once, like this:
the sum of every row, every col, every diagonal(including non-main diagonals) are ALL the same. for example, 14 + 20 + 21 + 2 + 8 = 19 + 8 + 22 + 11 + 5 = 1 + 24 + 17 + 15 + 8 = 19 + 2 + 15 + 23 + 6 = 65. you may calculate these 20 sums yourself, then, you'll know I am talking about.
This kind of squares (20
sums are ALL the same) is called POWERFUL MAGIC SQUARES. Your task is: given a
uncompleted square, count the number of powerful magic squares that can be
obtained by completing the square.
Input
The first line of the input contains a single integer n(1 <= n <= 15000), the number of test cases followed. For each case, there are five lines containing the uncompleted squares. Blank squares are represented as '--'. Filled numbers are always between 1 and 25. every test case is followed by a blank line except the last one.
The input format is always
correct.
Output
For each test case, print the case number and the number of squares obtained, like shown below.
Sample
Input Output
for Sample Input
|
2 1 7 13 19 -- 14 20 21 2 -- 22 3 9 15 -- 10 11 17 23 -- -- -- -- -- -- 1 2 3
-- -- 4 5 6
-- -- 7 8 9
-- -- -- -- -- -- -- -- -- -- -- -- |
Case
1: 1 Case 2: 0 |
Problemsetter: Rujia Liu, Member
of Elite Problemsetters' Panel