X, Y and Z are playing a game. There are certain number of matchsticks on a table. Each person has to pick up one matchstick and at most two matchsticks. The person who picks up the last matchstick losses. X, Y and Z play in that order one after the other, starting with X, till all the match sticks are picked up. Each person plays such that, to the extent possible, he does not lose even if the other two players collude. Q1. How many match sticks should X and Y respectively pick, in their first chance, so that Z is certain to lose if X and Y play with common objective of making Z lose? There were 7 matchsticks to start with. Q2. If there are 5 matchsticks at some point of time in the game, and you are told that Y later lost the game, then whose turn was to pick up matchsticks at that point of time? Q3. What is the smallest number of matchsticks greater than 5 at the beginning, that would ensure that Z will lose given that X and Y work towards making Z lose? __________________
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Q1. How many match sticks should X and Y respectively pick, in their first chance, so that Z is certain to lose if X and Y play with common objective of making Z lose? There were 7 matchsticks to start with.
a. (1, 1)
b. (1, 2)
c. (2, 1)
d. (2, 2)
Soln:
Option (a) is correct...
(x,Y,Z,X,Y,Z)=(1,1,2,1,1,1) or (1,1,1,2,1,1)
=>Z looses(it doesnt depend on whether Z pics 1 or 2 matchsticks)....Bt fo all other option dr remains chances for Z to win....
Giv ur best to d world.
Nd d best will cm back to u.....
Regards,
Dipanjan......
n/a
Q3. What is the smallest number of matchsticks greater than 5 at the beginning, that would ensure that Z will lose given that X and Y work towards making Z lose?
a. 7
b. 8
c. 9
d. 6
Soln.
(X,Y,Z,X,Y,Z)=(1,1,1,2,1,1)=(1,2,2,1,1,1) So Z losses whether he picks 1/2 matchsticks...
No. of matchsticks=7....
Giv ur best to d world.
Nd d best will cm back to u....
Regards,
Dipanjan.....
n/a
Q2. If there are 5 matchsticks at some point of time in the game, and you are told that Y later lost the game, then whose turn was to pick up matchsticks at that point of time?
a. X
b. Y
c. Z
d. Cannot be uniquely determined
definately now turn for z
because z pick 2 , x pick 2 so la st one pick by y and y lose game
Little Star
n/a
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