In how many ways two queens can be placed on a 8×8 chess board such that they are not able to attack each other (Queens can attack in the same row/column/diagonal) (i). one queen is black & other queen is white (ii). both queens are identical.

by shivamtripathi22 | Jan 18, 2024 | Uncategorized

(Q). In how many ways two queens can be placed on a 8×8 chess board such that they are not able to attack each other (Queens can attack in the same row/column/diagonal)? (i). one queen is black & other queen is white (ii). both queens are identical. Solution:- we...

In how many ways two identical kings can be placed on a 8×8 chess board such that they are not on adjacent squares

by shivamtripathi22 | Jan 18, 2024 | Uncategorized

(Q). In how many ways two identical kings can be placed on a 8×8 chess board such that they are not on adjacent squares? Solution:-  From the solution of previous question number of ways = 3612 (When kings are distinguishable) now in this question kings are...

In how many ways two kings one black & one white can be placed on a 8×8 chess board such that they are not on adjacent squares

by shivamtripathi22 | Jan 18, 2024 | Uncategorized

(Q). In how many ways two kings one black & one white can be placed on a 8×8 chess board such that they are not on adjacent squares?Solution:- Here we have following cases for placing the 1ˢᵗ king.Case(i): Lets 1ˢᵗ king be placed at one of the 4 corners of chess...

Consider a decomposition of an 8×8 chessboard into p non overlapping rectangles with the following condition:- Condition (i):- Number of white and number of black squares are same Condition (ii):-  If aᵢ is the number of white squares in the iᵗʰ rectangle then a₁ < a₂ < a₃ < .........

by shivamtripathi22 | Jan 16, 2024 | Uncategorized

(Q). Consider a decomposition of an 8×8 chessboard into p non overlapping rectangles with the following condition:- Condition (i):- Number of white and number of black squares are same Condition (ii):-  If aᵢ is the number of white squares in the iᵗʰ rectangle then a₁...

Consider a 6×6 square which is dissected into 9 rectangles by lines parallel to its sides such that all the rectangles have integer sides. Out of 9 rectangles what is the maximum number of congruent rectangle

by shivamtripathi22 | Jan 13, 2024 | Uncategorized

(Q). Consider a 6×6 square which is dissected into 9 rectangles by lines parallel to its sides such that all the rectangles have integer sides. Out of 9 rectangles what is the maximum number of congruent rectangle ?Solution:-Let us solve this problem...

Consider 5 points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or co-incident. From each point perpendiculars are drawn to all the lines joining the other four points. Determine the maximum number of intersections that these perpendiculars can have

by shivamtripathi22 | Jan 13, 2024 | Uncategorized

(Q). Consider 5 points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or co-incident. From each point perpendiculars are drawn to all the lines joining the other four points. Determine the maximum number of...