Qaunt - Matchstick Problem

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  • Topic: Pick operating system, Guitar pick, Game
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  • Published : March 5, 2013
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Harish and Sachin are playing a game of matchsticks.There are N matchsticks on the table to start with.Each player in his turn picks up atleast one matchstick and at most 8 matchsticks.Th two players takes turn alternately.The player who clears the table loses.Assume that each player plays intelligently with an objective of winning.The first move is made by Harish.No player is allowed to pass his turn without picking up any matchsticks,

Question 1:- If for some N,it is known that the number of matchsticks picked up by Harish in his first four moves were 6,4,3 and 6 resp. then how many matchsticks wud Sachin have picked up in his third move given that Harish wo the game? 1) 3 2) 5 3)6 4) Data Insufficient

Question 2:- If it is known that the game was completed in 8 moves (By each of the two playes),what is the maximum possible value for N? 1)63 2)71 3)72 4)81

Addition information for the following two questions:
Instead of minimum of one matchstick if each player has to pick up at least 2 matchsticks in his turn.The only instance that a player is allowed to pick up one matchstick is when there is only one matchstick left on the table.

Question 3:- It it is known that N is greater than 6 but less than 44,for how many values of N will Harish certainly lose the game,irrespective of how he plays? 1)4 2)5 3)6 4)8

Question 4:- If it is known that N is greater than 128 but less than 138 and that Harish picked up 6 matchsticks in his first move and eventually won the game then what is the value of N 1)137 2)133 3)134 4)Can't be determined

These type of problem can be solved by finding the number which will ensure the total # of picks of matchstick with each round. The required # is : =
in this case it is = 1+8 = 9
Q1) it is clear that Haris has to make sure, when he picks for the 1st time that, after the first pick the remaining Matchstick become of form 9k. i.e the total number of matchstick is = 9k+6 now evry round (ending with haris)...
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