Question

Suppose that there are 27 matches originally on the table, and you are challenged by your dinner partner to play this game. Each player must pick up either 1, 2, 3, or 4 matches, with the player who picks up the last match pays for dinner. What is your optimal strategy? (Describe your decision rule as concisely as you can.)

Answer 1

The person pickining the last matchstic looses and these makes the obvious explaination that the one looses takes the last 1 matchstick becuase if there are 2 matchsticks left then the opponent will take 1 match stick only to make the table has only 1 matchstick left.

The key is that all the players can match 5matchsticks in a round (a round means 2 persons take their chance)

So the key is that 5*5 = 25 (so after 5 rounds you can manage with 25 sticks)

So now if you pick 1 matchstick first is the key to win

Say., You pick 1 matchstick 1st

Then whatever your opponent takes , you have to take 5-matchsticks your opponent took

Say after that your opponewnt takes 4 then you take 1

Say your opponent takes 2 then you take 3 and so on

So that you can drag the match till 25 matchsticks picked and then force your opponet to take the last one

So., The key is that the first person takes 1 match stick and there after for the next 5 rounds it matches total 5 match sticks by taking 5-opponent's matchsticks so that 1+25=26 and force the opponent to take the last matchsatick.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!