I have to solve this question within the next 2 hours. Its an assignment and i need to be absolutely correct in order to earn the A grade. Here it goes. Q: There are x number of balls in the basket. Two players take turns to pick and remove either 1 or 4 balls from the basket. The person who picks the last ball wins the game. a) What should be the winning strategy. b) If we change the game and the person who picks the last ball loses, what should be the winning strategy. Can anybody help me?
This is tricky but i like challenges If i was a player and i could count the number of balls in basket i would for a start but: a) Wouldnt the winning startegy be to aim to get down to there only being 8 balls in basket? then no matter the possible combinations that occur as a result of the other players choice you are in the best postion to win b) This winning strategy would be like above to aim to get down to having only 3 balls left after you have your turn or multiples of 3 so 6,9,12 etc. again then no matter the possible combinations that occur as a result of the other players choice you are in the best postion to win I dont know the mathematical reasoning behind it but that is how i see it but could be wrong?
If the person who get the last ball will win the game, and the player must take from 1 to 4 balls. In this case, the strategy is ensure the balance of ball is 5 or Multiples of 5. However, if the person who get the last ball lose, the strategy is abit different, the balance shall be the 6 of multiple of 6.
I can't see any strategy until "x" is not defined as even, odd or exact number. The only thing you can do is for: a) to pick every time 4 balls. You have chance to win 50% or 80% if the other player picks every time 1; If you pick only one time 1 balls you decrease your chance to 20% for the current picking (if your opponent pick 4) and this don't give you bigger chance for the next picking b) to pick every time 1 ball. You have chance to win 50% or 80% if the other player picks every time 4; If you pick only one time 4 balls you decrease your chance to 20% for the current picking (if your opponent pick 1) and this don't give you bigger chance for the next picking So there is no strategy.