3

Part of 2019 Tuymaada Olympiad

Problems(2)

custodians in rooms of gallery, where the plan is like a chessboard (juniors)

Source: Tuymaada Olympiad 2019 junior p3

The plan of a picture gallery is a chequered figure where each square is a room, and every room can be reached from each other by moving to rooms adjacent by side. A custodian in a room can watch all the rooms that can be reached from this room by one move of a chess rook (without leaving the gallery). What minimum number of custodians is sufficient to watch all the rooms in every gallery of

n

n > 1

combinatoricsminimum valueminimumChessboard

custodians in rooms of gallery, where the plan is like a chessboard

Source: Tuymaada 2019 p3

The plan of a picture gallery is a chequered figure where each square is a room, and every room can be reached from each other by moving to adjacent rooms. A custodian in a room can watch all the rooms that can be reached from this room by one move of a chess queen (without leaving the gallery). What minimum number of custodians is sufficient to watch all the rooms in every gallery of

n

n > 2

combinatoricsminimum valueminimumChessboard