Katedra matematiky - Katolícka univerzita v Ružomberku

158 Tadeusz Ratusiński5. The winning strategyEveryone who plays a game wants to win. This intention of winning thegame is good situation for discovering reduction reasoning. Why ?Game seems to be easy. Starting position is the first flower at the bottomof the board (it’s marked with "S" on the picture 3 & 4). The goal of thegame is to reach the hive (at the top of the board - "F" on schema). Buthow should we play to manage to do this? There is winning strategy forboth of boards.By winning strategy we understand such a plan of proceeding, which leadus to victory independently on partner’s movements. Player must uncoverand use them to win in whole game. To do this he must answer the question"Where I have to put Bee to be sure that in my last movement I will reachhive (I will put Bee on finish line)?" Let’s look how he might discover thewinning strategy for left board (picture 3).Figure 3 - Meadow 1 Figure 4 - Meadow 2The correct answer for that question is "I have to put Bee on flowermarked as "A" at the top of the board". New question appears immediately"what should I do to put it over there?" And now player must discover thatthe fundamental point for this is to take position on one of flowers markedas "B" or "C". "But how to get to this position?" Strategic point for thissituation is the next flower "D". The next step of reduction indicate nextflower "E". The last question "How to made to put Bee on flower "E"?"is trivial, because "when I start I can move pawn to that position". Playerfinishes all steps of reduction and find out full winning strategy for leftboard. Those, who will begin game have to put Bee on flower "E" and nextjump to lucky flowers "D", "C" or "B", "A" and finally reach hive (markedas "F"). The player who begins as second should try to occupy any of the