an empty bag and a chessboard and unlimited supply of tokens
Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p4
October 8, 2022
combinatoricsgamegame strategy
Problem Statement
On a table, there is an empty bag and a chessboard containing exactly one token on each square. Next to the table is a large pile that contains an unlimited supply of tokens. Using only the following types of moves what is the maximum possible number of tokens that can be in the bag?
Type 1: Choose a non-empty square on the chessboard that is not in the rightmost column. Take a token from this square and place it, along with one token from the pile, on the square immediately to its right.
Type 2: Choose a non-empty square on the chessboard that is not in the bottommost row. Take a token from this square and place it, along with one token from the pile, on the square immediately below it.
Type 3: Choose two adjacent non-empty squares. Remove a token from each and put them both into the bag.