(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...
(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...
(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...
(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...
(Q). There are ‘n’ points in a plane. No three of which are on same straight line. All the possible straight lines are made by joining these ‘n’ points. (i) What is the maximum number of point of intersection of these straight lines? (ii)...
(Q). In how many ways 2 + and 2 – signs are filled into 4×4 cell where each cell can contain maximum one character such that each row & column can not contain same sign...
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