Latest self Aptitude Question SOLUTION: Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other.One of them is a special (gold) coin and the rest are ordinary coins. The goal is t

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(#M40002601) SELF question Keep an EYE

Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other.One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin tothe top by repeatedly moving the topmost coin to another position in the stack.Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i belowthe top coin (0 = i = 20). We will call this an i-move (thus a 0-move implies doing nothing). The provisois that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turnsneither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn thenthe player wins the game. Initially, the gold coinis the third coin from the top. Then find the valid game between alice and bob.
a) In order to win, Alice's first move should be a 1-move.
b) In order to win, Alice's first move should be a 0-move.
c) In order to win, Alice's first move can be a 0-move or a 1-move.
d) Alice has no winning strategy.

Solution

(b)In order to win, Alice's first move should be a 1-move....
reason:there are two possibility after 1- move by Alice:-
1. when bob takes 0-move....then the coin config is same ..... but now alice can neither take 1-move nor 0-move.... so she has to take 2 or greater move(let it be 2 move)............
now we have only one coin above the gold coin......now bob can neither take 1-move nor 0-move nor 2-move.... so she has to take 3 or greater move.......
but the move greater then 2-move brings gold coin on top....makes alice win...

2.now bob takes 2-move after alice's first move....... now thre is only one coin above the gold coin..... so Alice takes 0-move........now we have only one coin above the gold coin......now bob can neither take 1-move nor 0-move nor 2-move.... so she has to take 3 or greater move.......
but the move greater then 2-move brings gold coin on top....makes alice win...

This answer is given by ROHIT KUMAR and is the correct answer

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aniruddha mandal (12 years ago)

Solved Read Solution (3)

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yasaswini  (12 years ago)

Its just a simple logic which am giving. But its not the right procedure.. Bt it will work for this type of questions..
The answer is C

Check the condition in the last line of the question. If they had given that ",initially the gold coins the THIRD coin from the top" consider the position like first,third,fifth positions then answer will be third. If it is in even position then answer will be option 'd'.

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Nandita Pandey  (12 years ago)

Alice's 1st move should b a 0 move

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Mudhu Krishna Lalapet  (5 years ago)

a) In order to win, Alice's first move should be a 1-move.

Firstly, if Alice selects 0-move as first move, Bob will do 2-move then there is only one coin above the gold coin. Now Alice has to perform at least 1-move. Then she loses so Alice will not choose 0-move

Secondly, if Alice selects 1-move as her first move then there are two possibility after 1- move by Alice that Bob either take move 0 or ≥ 2
Possibility 1: When bob takes 0-move then the coin configuration will not change and now Alice can neither take 1-move nor 0-move so she has to take move ≥ 2

Let Alice take 2- move then she wins because there is only one coin above the gold coin.

Possibility 2: When Bob takes move ≥ 2 after Alice’s first move then there will be only one coin above the gold coin So Alice takes 0-move then the coin configuration will not change and Alice wins.

So in either possibility Alice wins.
So Alice first move should be a 1-move to win.

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