MathDB

Two types of pieces, bishops and rooks, are to be placed on a

10\times 10

chessboard (without necessarily filling it) such that each piece occupies exactly one square of the board. A bishop

B

is said to attack a piece

P

B

and

P

are on the same diagonal and there are no pieces between

B

and

P

on that diagonal; a rook

R

is said to attack a piece

P

R

and

P

are on the same row or column and there are no pieces between

R

and

P

on that row or column. A piece

P

is chocolate if no other piece

Q

attacks

P

. What is the maximum number of chocolate pieces there may be, after placing some pieces on the chessboard?
Proposed by José Alejandro Reyes González

Problem Statement