The "Missionaries and Cannibals Problem" is a classic river-crossing puzzle in which three missionaries and three cannibals must cross a river using a boat that can carry only two at a time. The challenge arises because if at any point the cannibals outnumber the missionaries on either side of the river, the cannibals will eat the missionaries. To solve the problem, players must strategize the crossings to ensure that the number of missionaries never falls below the number of cannibals on either side. This requires careful planning and consideration of each crossing to achieve the goal of getting everyone across safely.