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Correct CHOICE is (B) (1,6,3,8,3,2,4,7)

Best explanation: The FOLLOWING GIVEN OPTIONS for optimal solutions of 8-queens problem, (1,6,3,8,3,2,4,7) does not provide an optimal solution.

The correct option is (d) 5

Easiest EXPLANATION - The minimum number of QUEENS NEEDED to occupy EVERY square in n-queens PROBLEM is called domination number. While n=8, the domination number is 5.

The correct choice is (b) false

The EXPLANATION is: For n=1, the n-queen PROBLEM has a trivial and real solution and it is REPRESENTED by

Correct answer is (C) 92

Easy EXPLANATION - For an 8-queen problem, there are 92 possible combinations of optimal SOLUTIONS.

The CORRECT answer is (a) (3,1,4,2)

For EXPLANATION: Of the following GIVEN options for OPTIMAL solutions of 4-queens problem, (3, 1, 4, 2) is the right option.

Correct ANSWER is (d) backtracking

To explain: Of the following GIVEN APPROACHES, n-queens PROBLEM can be SOLVED using backtracking. It can also be solved using branch and bound.

Right OPTION is (b) 2

The explanation is: N-queen problem does not provide an OPTIMAL SOLUTION of only three values of n (i.e.) n=2,3.

Right CHOICE is (B) chess

For explanation: N-queens problem OCCURS in chess. It is the problem of PLACING n- queens in a n*n chess board.

The correct option is (a) n-queen’s problem

Easiest EXPLANATION - PLACING n QUEENS so that no two queens ATTACK each other is n-queens problem. If n=8, it is called as 8-queens problem.

Right answer is (a) True

Explanation: There are total 4 SOLUTIONS for the SIX queen puzzle and one FUNDAMENTAL solution while there are total of 10 solutions for 5 queen puzzle and 2 fundamental solutions.

The correct answer is (d) 0

To explain: There are in total ZERO SOLUTION to the 3 queen PUZZLE for 3*3 chess board. Hence there are no fundamental SOLUTIONS. For 8*8 chess board with 8 queens there are total of 12 fundamental solutions for the puzzle.

Correct answer is (d) 12

To explain: There are total of 12 FUNDAMENTAL solutions to the eight queen PUZZLE after removing the symmetrical solutions DUE to rotation. For 8*8 CHESS board with 8 queens there are total of 92 solutions for the puzzle.

Right OPTION is (a) Zongyan Qiu

For explanation: The FIRST person to publish the BITWISE operation method to solve the EIGHT queen puzzle was Zongyan Qiu. After him, it was published by Martin Richard.

Right answer is (c) 92

For EXPLANATION: For 8*8 chess board with 8 queens there are total of 92 solutions for the puzzle. There are total of 12 fundamental solutions to the EIGHT queen puzzle.

Right choice is (a) Edsger Dijkshtra

For explanation: In 1972, depth first backtracking algorithm was proposed by Edsger Dijkshtra to illustrate the EIGHT Queen PUZZLE. MAX Friedrich William Bezzel PUBLISHED the puzzle and the first SOLUTION to the Eight Queen Puzzle was given by Franz Nauck.

Right answer is (d) n

Easy explanation - The EXTENDED version GIVEN by FRANZ Nauck of the Eight Queen Puzzle was for n queens on n*n square chessboard. EARLIER the puzzle was proposed with 8 queens on 8*8 board.

The CORRECT option is (a) FRANZ Nauck

To explain: The FIRST extended version to the EIGHT Queen Puzzle was given by Franz Nauck in 1850. Max Friedrich William Bezzel published the puzzle in 1848.

Correct option is (a) 1850

For EXPLANATION: The FIRST solution to the Eight Queen Puzzle was given by Franz Nauck in 1850. MAX Friedrich WILLIAM Bezzel, who was a German chess COMPOSER by profession published the puzzle in 1848.

The correct option is (a) Franz Nauck

For explanation: The FIRST solution to the Eight Queen Puzzle was given by Franz Nauck in 1850. While the first Eight Queen Puzzle was PUBLISHED by Max FRIEDRICH William Bezzel, who was a German chess COMPOSER.

Right ANSWER is (a) Max Bezzel

To explain: The first EIGHT Queen Puzzle was published by Max Friedrich William Bezzel, who was a chess COMPOSER by profession in 1848. He was a German chess composer and the first person to publish the puzzle.

The correct ANSWER is (a) n-queen problem

The best explanation: The problem of placing n-QUEENS in a chessboard such that no two queens are VERTICAL or horizontal or diagonal to each other is an n-queen problem. The problem only EXISTS for n = 1, 4, 8.

Correct option is (b) subset sum problem

Easiest explanation - Subset sum problem is the problem of FINDING a subset using the backtracking algorithm when summed, EQUALS a given INTEGER.

The correct answer is (C) Backtracking

Explanation: Backtracking is a GENERAL algorithm that EVALUATES partially CONSTRUCTED candidates that can be DEVELOPED further without violating problem constraints.

The CORRECT CHOICE is (d) Fortran

The explanation is: Backtracking ALGORITHM form the basis for icon, planner and PROLOG whereas fortran is an ancient assembly LANGUAGE used in second generation computers.

The correct option is (d) CROSSWORD

The best I can explain: Crossword puzzles are BASED on backtracking approach whereas the rest are travelling salesman PROBLEM, KNAPSACK problem and dice GAME.

Correct choice is (c) COMBINATORIAL problems

To EXPLAIN: BACKTRACKING approach is used to solve complex combinatorial problems which cannot be SOLVED by EXHAUSTIVE search algorithms.

Right answer is (B) false

Best explanation: The leaves in a state space tree can either REPRESENT non-promising dead ends or complete solutions FOUND by the ALGORITHM.

The CORRECT CHOICE is (a) Depth-first search

The explanation is: A state-space TREE for a backtracking algorithm is CONSTRUCTED in the manner of depth-first search so that it is easy to look into.

Correct OPTION is (b) PROMISING

For explanation: If a node has a possibility of reaching the FINAL solution, it is called a promising node. Otherwise, it is non-promising.

The CORRECT ANSWER is (B) It continues searching for other possible solutions

Easiest EXPLANATION - When we reach a final solution using a backtracking algorithm, we either STOP or continue searching for other possible solutions.

Right option is (a) State-space TREE

For explanation: BACKTRACKING problem is solved by CONSTRUCTING a tree of choices called as the state-space tree. Its ROOT represents an initial state before the search for a SOLUTION begins.

Right option is (d) travelling salesman PROBLEM

The best explanation: N-queen problem, SUBSET SUM problem, Hamiltonian circuit problems can be solved by BACKTRACKING METHOD whereas travelling salesman problem is solved by Branch and bound method.