## GAME31 - The game of 31

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is played with a deck of 24 cards: four labelled each of 1, 2, 3, 4, 5, 6. The cards in the deck are
visible to both players, who alternately withdraw one card from the deck and place it on a pile.
The object of the game is to be the last player to lay a card such that the sum of the cards in
the pile does not exceed 31. Your task is to determine the eventual winner of a partially played
game, assuming each player plays the remainder of the game using a perfect strategy.
For example, in the following game player B wins:
Player A plays 3
Player B plays 5
Player A plays 6
Player B plays 6
Player A plays 5
Player B plays 6
Input:
The input will consist of several lines; each line consists of a sequence of zero or more digits
representing a partially completed game. The rst digit is player A's move; the second player
B's move; and so on. You are to complete the game using a perfect strategy for both players
and to determine who wins.
Output:
For each game, print a line consisting of the input, followed by a space, followed by A or B to
indicate the eventual winner of the game.
Example Input:
356656
35665
3566
111126666
552525
Example Output:
356656 B
35665 B
3566 A
111126666 A
552525 A

The game of 31 was a favourite of con artists who rode the railroads in days of yore. The game

is played with a deck of 24 cards: four labelled each of 1, 2, 3, 4, 5, 6. The cards in the deck are

visible to both players, who alternately withdraw one card from the deck and place it on a pile.

The object of the game is to be the last player to lay a card such that the sum of the cards in

the pile does not exceed 31. Your task is to determine the eventual winner of a partially played

game, assuming each player plays the remainder of the game using a perfect strategy.

For example, in the following game player B wins:

Player A plays 3

Player B plays 5

Player A plays 6

Player B plays 6

Player A plays 5

Player B plays 6

Input:

The input will consist of several lines; each line consists of a sequence of zero or more digits

representing a partially completed game. The rst digit is player A's move; the second player

B's move; and so on. You are to complete the game using a perfect strategy for both players

and to determine who wins.

Output:

For each game, print a line consisting of the input, followed by a space, followed by A or B to

indicate the eventual winner of the game.

Example Input:

356656

35665

3566

111126666

552525

Example Output:

356656 B

35665 B

3566 A

111126666 A

552525 A

hide comments
 Ankit Sultana: 2015-05-26 21:29:19 getline gave me a couple of wa :/ PS: My AC solution doesn't print anything for 'zero digits' gourav pathak: 2014-12-26 10:44:16 brute force solution passes in the given time limit strings: 2013-02-07 16:38:11 please explain i/o... is there blank line after every input?? Do we have to process a blank line?? Should we print a blank line after every case o/p ?? Aditya Pande: 2012-12-21 09:11:19 nice problem. learnt a lot about game theory...:) AC Srinivas: 2012-08-15 05:19:59 @skmiiita case 3: (current sum: 20; to get 31-required 11 to finish) player A will play 4 making current sum 24, player B can only make sum of 25-30(with cards 1-6), so player A can make it 31 and finish. Last edit: 2012-08-15 05:29:24 skmiiita: 2011-11-26 19:26:02 can anyone explain case 3. i mean it is similar to case 1 and case 2 but answer is different. Buda IM (retired): 2011-11-14 14:13:46 Please clear out IO matters. Are there empty lines between every test case, and should we print the empty lines after each output. Ankur Brahmbhatt: 2011-08-30 12:30:33 should the output for zero digits be:" A" and for input:1 output:"1 B"? Naman: 2011-08-26 22:18:07 shouldn't be output of 4th and 5th example be B wins?? 4th-B picks 1 (sum 31) => A loses in next turn 5th-A picks anything(1,2,3,4,5,6) B picks counter(6,5,4,3,2,1) (sum 31) => A loses in next turn Edit: Sorry I forgot "deck of 24 cards" Last edit: 2011-08-27 21:13:44

 Added by: Andres Tellez Date: 2011-08-22 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64