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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 < .........

(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

(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

(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...

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) Taking point of intersection of these straight lines as vertices of triangles then what is the maximum number of triangles that can be formed?

(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)...