CODEWITHSUNDEEP
mathoptimizationcombinatoricsn-queens
user5492770
user5492770

Reputation: 377

maximum number of non attacking pairs of queens in 8 queens

Maximum number of non-attacking pairs of queens in 8-Queens problem is given by 8 × 7/2 = 28. Can someone explain how it is 8x7/2?

Upvotes: 3

Views: 3086

Answers (2)

user2256398
user2256398

Reputation: 76

A non attacking pair is when two queens don't attack each other.For max condition no queen attacks any other queen, so number of non attacking pairs

1st queen would have = 7 2nd queen would have = 6 (exclude the pair with the 1st queen as its already counted in step 1)

Similarly, 3rd queen would have = 5

Thus, total number of non attacking pairs for 8 queens would be = 7+6+5+4+3+2+1+0 =28

Upvotes: 3

Kenan
Kenan

Reputation: 14104

Here is another thought process: We have 8 queens and you want to know every possible attacking pair on the board so we have 8 choose 2 or 

8!/((8-2)!*2!) = 28

Upvotes: 1

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