Please provide a step by step solution ,

Introduction to Design Analysis and Algorithm Ch 3.4 problem 9 Please show step by step solution

problem says

Eight-queens problem Consider the classic puzzle of placing eight queens on

an 8 8 chessboard so that no two queens are in the same row or in the same

column or on the same diagonal.How many different positions are there so that

a. no two queens are on the same square?

b. no two queens are in the same row?

c. no two queens are in the same row or in the same column?

Also estimate how long it would take to find all the solutions to the problem by

exhaustive search based on each of these approaches on a computer capable

of checking 10 billion positions per second.

Notes :

Actually I am posting this question fr the second time

Are they 3 cases to to solve or 4 cases or just 1 case to solve i,e in the problem head it says

no two queens are in the same row or in the same

column or on the same diagonal. (This statement overrides a, b ,and c) should we follow this statement or should we should ignore it and answer ((3 questions)) a b and c

Also in a , ba and c

a. no two queens are on the same square? it is logic why he mentioned that ?does it mean we can allow it in b and c ? I do not think so

b. no two queens are in the same row? does it mean we can allow same column and same diagonal ?

c. no two queens are in the same row or in the same column? does it mean we can allow same diagonal ?

Anyway I am really waiting to know the step by step answers

Thanks