# Is there a winning strategy for Atul and Bhola?

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Atul and Bhola are prisoners. The jailer have them play a game. He places one coin on each cell of an 8x8 chessboard. Some are tails up and others are heads up. Bhola cannot yet see the board. The jailer shows the board to Atul and selects a cell. He will allow Atul to flip exactly one coin on the board. Then Bhola arrives. He is asked to inspect the board and then guess the cell selected by the jailer. If Bhola guesses the correct cell among 64 options, Atul and Bhola are set free. Otherwise, they are both executed. Is there a winning strategy for Atul and Bhola? (They can co-operate and discuss a strategy before the game starts).

posted Jul 11, 2014
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Consider a two player coin game where each player gets turn one by one. There is a row of even number of coins, and a player on his/her turn can pick a coin from any of the two corners of the row. The player that collects coins with more value wins the game. Develop a strategy for the player making the first turn, such he/she never looses the game?

Note that the strategy to pick maximum of two corners may not work. In the following example, first player looses the game when he/she uses strategy to pick maximum of two corners.

``````Example
18 20 15 30 10 14
First Player picks 18, now row of coins is
20 15 30 10 14
Second player picks 20, now row of coins is
15 30 10 14
First Player picks 15, now row of coins is
30 10 14
Second player picks 30, now row of coins is
10 14
First Player picks 14, now row of coins is
10
Second player picks 10, game over.

The total value collected by second player is more (20 +
30 + 10) compared to first player (18 + 15 + 14).
So the second player wins.
``````

Suppose two player, player A and player B have the infinite number of coins. Now they are sitting near a perfectly round table and going to play a game. The game is, in each turn, a player will put one coin anywhere on the table (not on the top of coin already placed on the table, but on the surface of the table). And the player who places the last coin on the table will win the game. Given player A will always move first. Suggest a strategy such that player A will always win, no matter how player B will play?

Alpha and Beta are playing bets. Alpha gives \$10 to Beta and Beta deals four card out of a normal 52 card deck which are chose by him completely randomly. Beta keeps them facing down and take the first card and show it to Alpha. Alpha have a choice of either keeping it or to look at the second card. When the second card is shown to him, he again has the choice of keeping or looking at the third which is followed by the third card as well; only if he does not want the third card, he will have to keep the fourth card.

If the card that is being chosen by Alpha is n, Beta will give him . Then the cards will be shuffled and the game will be played again and again. Now you might think that it all depends on chance, but Alpha has come up with a strategy that will help him turn the favor in his odds.

Can you deduce the strategy of Alpha ?

+1 vote

There is a prison with 100 prisoners, each in separate cells with no form of contact. There is an area in the prison with a single light bulb in it. Each day, the warden picks one of the prisoners at random, even if they have been picked before, and takes them out to the lobby. The prisoner will have the choice to flip the switch if they want. The light bulb starts in the Switched off position.

When a prisoner is taken into the area with the light bulb, he can say "Every prisoner has been brought to the light bulb." If this is true all prisoners will go free. However, if a prisoner chooses to say this and it's wrong, all the prisoners will be executed. So a prisoner should only say this if he knows it is true for sure.

Before the first day of this process begins, all the prisoners are allowed to get together to discuss a strategy to eventually save themselves.

What strategy could they use to ensure they will go free?