TopCoder Statistics - Problem Statement

Problem Statement

Yvonne and Zed have a rectangular array of lightbulbs. Each lightbulb is either on or off. You are given the String[] board that describes their current states: '1' represents on, '0' off.

Yvonne and Zed use the array to play a game. They take alternating turns, Yvonne starts. In each turn the active player does the following:

The player must choose a lightbulb L that is currently on. If the player cannot do that, they lose the game.
The player must turn lightbulb L off.
The player then may choose another lightbulb L'. This lightbulb must be either somewhere to the right of L (in the same row) or somewhere downwards from L (in the same column).
If the player did choose L', they now must toggle it. (Turn it on if it was off, or vice versa.)

For the given board, count all winning moves for the player whose turn it is.

Definition

Class:: LightbulbGame
Method:: countWinningMoves
Parameters:: String[]
Returns:: int
Method signature:: int countWinningMoves(String[] board)
(be sure your method is public)

Constraints

board will contain between 1 and 50 elements, inclusive.
Each element of board will contain between 1 and 50 characters, inclusive.
All elements of board will have the same length.
Each character in board will be either '1' or '0'.

Examples

{"000", "000", "000"}

Returns: 0

All lightbulbs are off. The player immediately loses the game.
{"0000", "0100", "0000"}

Returns: 1

A single lightbulb is on. The only winning move is to turn it off and to refuse to toggle another lightbulb.
{"00000", "01001", "00000"}

Returns: 1

Two lightbulbs are on. As they are in the same row, the current player can win by choosing the lightbulb at row 1, column 1 (using 0-based indices) as L and then the other lightbulb as the L' to toggle. It can be shown that there are no other winning moves from this situation.
{"10", "01"}

Returns: 0

Two lightbulbs are currently on and two are off. We can work out all possible ways this game can play out to see that if the opponent plays optimally, the current player will lose regardless of the first move they make.
{"1111", "1110"}

Returns: 3
{"1101","1110","1011"}

Returns: 7
{"1"}

Returns: 1
{"0"}

Returns: 0
{"01"}

Returns: 1
{"10"}

Returns: 1
{"11"}

Returns: 1
{"0","1"}

Returns: 1
{"1","0"}

Returns: 1
{"1","1"}

Returns: 1
{"11","11","11","01","00","01"}

Returns: 5
{"011001100","111000010","111001010","111011011","110001110","100001111","011100011","001000011"}

Returns: 31
{"10010","10100"}

Returns: 3
{"101100001","000100010","100101100"}

Returns: 3
{"1110001","1010110","0110100","1110010","1110011","1100011","1100110"}

Returns: 23
{"0111010111","1100100111","1101001111","0110110100","0011001010","0010111101"}

Returns: 27
{"11","00"}

Returns: 3
{"10111011","00110110","10100011","00101011","01010100","00000000","00110110","10100001"}

Returns: 11
{"111111","100101"}

Returns: 9
{"00110101","11000011"}

Returns: 1
{"100","100","110"}

Returns: 1
{"1100","1011","1011","1110","1011","0010","1101","1100","1100"}

Returns: 13
{"1101","0001","0110","1101"}

Returns: 3
{"100010000","011001110","011011110","111011010","000000111","100111000"}

Returns: 5
{"0000","0011","1000","0001","1111","1100","1111","1111","1101","0110"}

Returns: 13
{"0110011001","1101111000"}

Returns: 3
{"1011","0100","0010","0011","0100","1011","0100","0110","1101","1011"}

Returns: 7
{"001110","001110","100100","110100","011010","000011","110011","000110","011110","011011"}

Returns: 7
{"0100000","0110110","1100100","1111011","1101011","1110001"}

Returns: 19
{"00101","01110","11000","11000"}

Returns: 7
{"00110001","10111110","01000010","10101011","00000001","01001101","01000011"}

Returns: 17
{"1","0","0","1","0","1","1","0"}

Returns: 1
{"1","0","1","0","0","0","0","0"}

Returns: 1
{"1110100110","1100111101","0011011011","0111101100","1000101110","1000011011"}

Returns: 13
{"1001100101","1010010110","1101000010","1100000011","1101110011"}

Returns: 9
{"0010","0001","0100","1101","0100","1101","0101","0100","0101"}

Returns: 3
{"110000","111110","110101","110000","110110","000010","001100","011101"}

Returns: 7
{"1","1","1","1","0"}

Returns: 0
{"000","011","001","000","111","010"}

Returns: 3
{"1011000010","0101111001","1000001000","0111100110","1110011101","0100100001","0101000101","1011001110","1001000000"}

Returns: 3
{"10011100011101011001011001111111101111110100011","11110111111011011011111110110111001111110101111","11111111011110101001111101010111101111001101111","11110101111111110001111111011111101101001101111","01011101111110101111111111111111111111110111010","11100011101001011111110111100111100111110111111","11110001111111010100100001110100111111101110101","10001011001111011111111010111111111110111011010","11101001111101111011101001111111111101011111111","01111111110111111101111110111111110110111111111","11011010101111110011111111111101111101110110111","11111111111111011111111101111110110111111110100","01111011111101111100101010101111011110000110111","11111101011110110111111111110111111011010011111","11101111101011110111110110111111110111111011111","11010011111111110101011111111111110011111011111","00110011011111100110101111110111100101111111001","11111001101111111011111001110011111111111111111","01100111111111000110111111101110111100101000101","10101110011111111011111011110011100111110111111","10111111111111111111001111101011110101111111011","00101111011111011110111011111011011111111101010","11111110111111111111101111111111110011111111111","01011011110111111111100101110111111111011110110","11110111101111110111101111111111111111111111010","10110011111110111101111111111101111101010110000","11011111110111111111110011011111111110111111111","10011001110010111111110111110010100111101111111","11011111010110111011010101111111110111111011011","11111101110111110111111111110111101010101110111","11111111111101111101111001110010111111001000111","00101111111111111110110111101110011100110111110","11111011001101111101111101111111010111010111111","10110001111111011101101111110011111110111101110","11010011011111011110111101010111110011000111010","11111111110100000111111111011111110111011011110","00111111111010111111111111111111110111111101101","11101110010111111101010111101101111000111011111","11010110001111111111110111111111111111010110011","11111111111111011110111110110111110111011011101","11111110101010111011111011011110111111111111011","10110110111110011101101111110010110111111011001","00110110111000101010111100111111110100100100111","10111111111111001111100101100001111101111111101","01011101111111011001110001111101101001111110100","10110111100111111110110101101101111111111110111","10111111010101111010110011010011010111101010001","10011011101111110111100111111001100111111111111"}

Returns: 1127
{"1101000010100010001000001011100101011000001000000","0111101011000000010101100001110000010000100110001","1011000011000000010101001000011001000001000010011","1010101001100000100011001000100100010010111001100","1111010000000000100010000000100000000100000000010","1110000000001010000001000110100010000101000011111","0010101101000011100110001110001000100001001001000","1010100011000000010000110001111010000001000100000","0011011100010111000000001001101000111000100001100","0100100011000010100000010000010100100010010111000","0000010000000100011100100100100110000010000001100","0001111000000110100001010000010110010100010010011","1100000000000001100110010000001010000010110110010","0101000100100000011011010101100000000100000000101","0010000011011000010000000000000001101100001000000","0011010000110110111000010001001011010001001100100","0000001010000111101000011000000111000000011000000","1000000000101001100010000110100100001111111000110","0010101111000000000001011110110100000001010010100","1100000100100010010000000000000110001000010101000","0000001001001010101000100001001011111010101000001","0001100110010000010000000001000010010010001111101","0010001000010001000000110111010110110000000010011","1001011100111110001001100000000111000010001110101","0010101000001101010110100000100000111001000100000","1101010001001000001001010100011000110000100010000","0000001101100001010001000000010100010010100111101","1101010111100101101000000000000011001000000000000","1000000001100010000000111010001110010011010001001","0000001010010000100100010000000000001010000100011","0100000010000100010101100100010000001011110101000","0000111100000011000101000001100011000101000000001","0100011000100010000001001000100001000000100111100","1100100100000100000000100000000000000100110010101","0100101000010001000110000010000101110011110000000","1100000110000000000001100000100100101100101000100","0000100010001100110000000110100010000000010010100","0010000001001000000000010010000000110000001010001","1001000010101011000100011000010001110011010100010","0000100010100001010001010000000010100000101100001","1001000000010100001001010100101011110100110010101","0100101101000000111000010000000100010110000110110","0010001011000010000100000000101011100000110100000","0010000000010000000000111000000010001000000000100","0001010100100100010000100010010110010010001010100","0001101110110110100010010101000000111100000001010","1000101000000100000100100011110011100000101000101","0001001001000101010001110000011000010110000001001"}

Returns: 23
{"11111111101111011110111111111111011101110011011111","10101111111101101111101111010101111011110000111101","11111011110101110111111111111111101011110101111111","11101111111111101111101111011111111111111011110111","11110101011111111111101110111010101101111111111110","11111111110111011111110011101011111111100001111110","11111111110101111111010111101111101111101111110111","11111111011101111111101010011111101111111011111101","11111111111101111111111111110111111111111110111110","01111111101111111111111101111101110111011111011111","11000111111111111110111111100110111110010100111011","11111111011111111111111000111011111111111111010111","11110111011110110111110001110111110110111111111110","11110111001111111111111111111111110111110111111011","01111111111111111110110111101110101111011111111101","11111111111111111010111111110010111110111111001011","11111010111101111111111110111111010100111101111111","01111111111010111111111101111101111111111110111111","11001110011111111101011100110101011111110101111111","11110111111111110111111111110011111111111011111111","01111011111011111110111111110011110111111111111111","11111100110111111111111010110111011111110111011111","10111111111011111111111111111111111111011011111111","11011111111111011111101011111011011111110111101111","11110111001111101111110111101111111011101100111111","11100011111111011111111011111110011100011111111111","11111111111110111111111010111111111111111110111011","11101111111111111111111011111110011111111111111111","11111110111111111111011111111101111001111111111111","11111111101110110111010111011111110111111111111111","10011011110100111101111101110101110100111100111111","11111101011010111101111111111111110010111110111111","11110110111111111111111011110111111111111111111111","01111100111111101111111111111001011111101111111111","11111111111101100011110101101111110111001111110111","11111111110111111110011111101111111111111101111111","10111111111011111011101111111111110011111111110011","11111011111101111111111110011111101110111011111111","10001111111111111111111011111111110111110111111111","01111111101101111111111101111111101111110111111111","11101110111111111101111111110111111011111111111111","11111111111101101111111110101111101111111110111111","11111111111111111111111111011011011111111011100110","10111111111111111111111110101011111101111111111111","01111101101110111110110110111011011111111111111111","01111111111111111111100111110101111101101111111111","11101110011111101111111111111101110111111111110111"}

Returns: 29
{"110000011111111011111010110101011111111011101000","111100110101111000110100011111101011111110101110","111001110111111110111001001011001010010100001111","000010011111011101111001010011010001100101001110","110111111011011101100001111111011010110101011101","110011001001111110111001111110001110001100111101","111011110101111011110011001001011110100010110110","111111111011100110111111001011111000010001010101","111001011011110111001111111110101111011110110011","101101100111111100100011011011110101111010110100","100011111011001110011111111110111010111111001011","110100011110001111000011010011111011100001010010","100101001011101000011001101111010011111110011111","101001110101101010111100111110111001101010110011","001111001101001111110010010111001001010100110111","111111110010001011111100100000110111001110110010","101100011110111001010111001011011001001011011100","110011111111101100111010001100110111111111110111","010110010000011111111100111111110111100111101110","111101110111011010011101011111111001111011111111","001011101010111101101011010000010010001100011011","111110111001100110100110111011010111010011111111","000101111110011111110011000000111011111101011111","100111111000011010010101111101110110000110100011","110011110011100010110011110010110111100011111111","100011011110111001011100011011111011101101100111","011101010110111011011111110100100111000111111100","110001111100111010110111011111001100111101001001","011111111010110010111011011101110100111001101101","111110011100111001101001010111000110100110100110","001100110011101110000101111000011100011010110101","101111111011000111110011000010011110101101011110","111010000100011111110111101001101011110100110011","111001001110101110101110011111111111100001010010","101101011100111111010111010111001011001101101101","111111010011111100010000001100101000011001111111","111010111011111111000011110011111110100111111101","010110001001010011111011010010101111011011010001","101011110100111110011000100111101111111101100111","111111011011111010010011111111111110100010010111","011010011011001011100111110010111100001100100101","011101111111010100101011110101110011110101101111","011000101111100011111111011100011101111011001111","111011101101101110101111111111010110011100111110","101001011010100110111001101110110011010100111011","100111111110110010101100110011110100100010111110","100010100010011101011001110111101100111110111110","101111100001111010101011110101100110101001010110"}

Returns: 1375
{"1111111101111011111111111111111111111111111111111","1111111111111110111111101111111111101111111111110","1111111111111111111111111111111111111111111111111","1111111111110111011111101111110111111111011111111","1111111111111111111111111111111111110111111111111","1111111111111111111111111111111111111111111011111","1111111111111111111111111111111111111111111111111","1111111111111110111110111111111111111111111111111","1111111111111111111101111111111111111111111111111","1111111111111111110111101111111111111111111111111","1011111111111111111111111111111111111111111111111","1111111111111111111111111111111111111111111111111","1111111101111111110111111110111111111111110111111","1111111111011111111111111111111111111111011111110","1111111111011111111111111111111111011111111111111","1111111111111111111111101101111111111111111111111","1111111011111111111111111111111111111111110111111","1111111111111111111111111111111110111111111111111","1111111111111111111111111111111110111111111111111","1111111111111111111111011011111111111111111111111","1111111111111111111111111111111111111111111111111","1100111111111111111111101111111111111111111111111","1111111011111111111111111111111111111111111111111","1111111011111111111111111111011111101111111111111","1111111111111111101110111111011111111111111111111","1111101111110101111111111111111111111111111111111","1111111111111111111111111111111111111111111111111","1111111111111111111110111111111111111111111111110","1111101111111111111101111111111111111111110111111","1101111111111111111111111111111110111111111111111","1111111111111111111111111111111111111111111111111","1101111111111111111111111111111111111111111111111","0111111101111111111111111111111111011111111111111","1111111111111111111111111111111111111111111111111","1110111111101101011111110111111011110111111111111","1111111101111111111111111111111111111111111111111","1111111111101111111111111111111111111111111110111","1111111111111111111111111111111111111111111111111","1111111111111111111111111111111111111111111111111","1111110111111111101111111111111111111110111111111","1111111111111111111111111111111111101111111111111","1111111111111111111111111111111111111111111111111","1111111111111111110111111111111111111111011111111","1111111111111111110111111111111111111011111111111","1111111111111111111011110111111111111111111110110","1111111111111111111111111101111111111111111011111","1111111111111111110111111111111111111111111111111","1111111111111111111111101111111111111111111111111","1111111111111111111111111111111111111111111111111"}

Returns: 35
{"100101001100010000011100000010011001111110101101","100101011101001010000110100100001100111000111000","100000011011010000010001000000110000101111100101","001001001010000000010101010110101110111000000111","000011011011100000100110000000000000010100010011","011000000001011010100101110111000000001101010000","101101010101110010001000010000101100000100001011","101010010000100110001011100010000110010100000101","110111000001111000100110111011000010000010010000","010011010001101100001010010000001111000010000100","000000101000101001000001100101010010100000011011","011111001011001100001101111000100000100111110001","011010000000100100000100111000010010111000001010","010110010000011110011101011111011101100010001001","000001110110000110111011101101101000000111000000","100000110001000001001000000010011000101100000010","110001110101000011101100111110110000100011010000","100010100100010001011101010001110000000010100101","100010001100111111110100000110000111101000001001","111101001100101011010101000001010110010100010000","110100100100100000000011101101000100000000110000","111100000100101000000101000001000001010000011001","101001101001110010001001011100001001111110000111","011010001000101001111001000010000000000101100100","011001010001011001001000010000001001010000010001","101100000000010110100000111001111100010110010111","110000100101011010011001000110111101101101110100","000110001001010101101011010101111101000000000000","011100000011101001000100010101100111101011001101","110001000111100101100001000010010001000011000001","010110010001001001100000010111111001000100100000","110101000000001010000100010001101000110110111100","001000001001101001000000011001001100010000100000","100000011101000010011010000111111010111001000010","110101000001110100100010100100100100110000000110","001011000001011110000011010010011000010001010001","000110100100100011001011001101101001111000110111","100100100101001010101100000010001010100000011100","000001010100000100011111001100001000100000000101","100001000010111000001001100001001101001010000011","011111111000100010000101100100000111110100101111","011000001000011000010101101111000000000000110100","011101001011001010100111111100110001010001000110","100011010111100010010101101000001001000101100010","110000111100010010101011001000100001001010010001","010001110001101001001101101000100000110001100100","011000101000110110000101101101010000101010000100","000100001111010100100011010111010010100001000100"}

Returns: 617
{"00101000101111101100000000111000000101011011011100","00110101101100101001100110110011011000100000110101","10000110001011001010010110001010011100011100101010","00000101100000110011010100111000110111000101100010","01000010101010011001111001001001101001000000100000","11111000000001010010000011011011000000011011000101","11000010000111101010101000000100110101101100000100","00100001101110110011111010010010010000010110011110","10010000000100100001010100010000000010100110101100","01011001000110000001000010111000000010010110110010","00010001000101001011000100001101111101000101011000","01110101100101100111110000011100110111000010100100","00111001101010110100000001011101010011110011000110","01001001000111011111001100101111100110000100011011","00001011100100111000100010010010111100010011110000","11100000101110000000010100110110010000101000001101","10000001000110111011001000110001010100001001101000","00011101010001101110010110000101000000111010110001","10100011001001000010111100101111110000101010000100","11000001101011100001001000100000000100001111011000","11100000000000101111000000001101000011100101110000","10010000001100110001101001101101011110000110010000","00011110010000100000101001000010000010010000110001","10101010100011101100000111010000000110101111101110","01000100001000010001001110000111111000100000000001","10001011010100101001001101000111001010100000110110","00100100011001000111001001000100000001110001110110","10010010110001010000000111100001001111010001000000","11000001001110100100100010010111110100000000101100","10100101101001110001110101000000010010010100100100","10010000000110100000000111101010000101100001100101","01110001110001100010011001000000101110010000000100","10000100001000110011110000011000101000100000100000","00011010000010011101101100010010101010000111000010","10101110011100101100101000001000000000110010000000","01100000010011011011000010110101110000100000000001","00011100100110010010100011010010101111001010010111","10101010100010110000111110101110101010000100010000","01001000001111101001110110000111010010001001010100","00000101101001011010000000110000111111010100100111","01001001100001011010001010101000110100000001000000","11000001110000100110011101000111011000000101000011","00010101000001010100010011100011111101101111110011","00000001110000000000100000100001100011000000000001","11001101000111001111000001101010110101100001101111","10000001001110001110000010111110000000100000000000","00010011000000000011001011111110110000101001011000","10011000000100111001000010100001000000100001000011","00110110010100101101001000000000001010010100000110"}

Returns: 27
{"0111110111101100110111101010111111100000011011011","1000011101111001101111101100010011011001001011111","1111010000101111011111111100111010100001101010111","0011011101000110111101100010101110001100111000011","1101001011101110110110101110111111000101011011011","1001111101000111111111011001100100110001000000110","0011000110100111011001110001100000111001100011010","1111111001001110101100100011110110011110001001111","1010110101101010011010101100111111001110101110110","1010001011111011011111011011000001110010110011111","0000110010011111110100101111010111010000111001111","0011000111011111100111101111111100101011101101111","0011111100101111011001110000010110101100000101111","1001100010110011001011100010111011001100101010111","1111011011001100011101010011011001110111111110001","1010101000011100011100111100001100101110011110100","1111111101100100101111111011010011011101001011001","0111010111100000110101111000010011100011010110101","1011111111110010101110111010101010111000111110010","1001001111101100101100101111000001101100001111001","0111001111101100101100100011111110011001010111010","1011100001010101001010001010111010100101101000101","0100001100100000010111101010111100010011100111101","0110101111111111011110101111111101011110110001100","1110110101111011001111111111000111111110000101011","1100000001000100100110111011101010111010101111001","1110010110110101001110100100000101010001101100101","1100110100101101000000010111101101101111110000001","0100111110110011001100101101011110110001100000110","1101100001100001110001000001001011101100111000011","0100101111011100111110010110001011101101010010011","1001111000010101010111101001100001100001100111100","1001111111011110101101111011101011111001000001000","0111000011111101111110000110101011011101000011110","0111001100011001110101110110100011001111010110011","0000100001110101011011101010011010011001011100100","1101111001000110010110110111001010000011101111000","1101011000111110011011001001100000000110010101101","0011110011110111101111110010101001101111010101001","0000010101110110010110100110111010110100111001001","0100000001110010101101011010000110110111001000000","1110010100001001111111111111100011001111111111011","1001001101100011101111011001101101101101011110101","1010101011001100111110110011101110000111111011101","1111001110101010010110011010100110110011010001011","1001111010110000111011011110101011111110010111011","1010110000000011010100011101000011110111100100111","1101010110000111110101111110100111001010111101110"}

Returns: 21
{"0001011101100001000001100001001001011101110111010","1011101111011101011101011110001010000001100010110","0011010101000000100001110110011101000000000000000","0110000101100111010100001100000110001010111100011","0100000110110001001010001010010100110111110011011","1001111100010000101001000101000011111010001011000","0011001110001000010011101001010001011000000110011","1011000100011100101001101000000100101110011010000","1011000100011101111101100111001101011000010011011","1001110010100111011110010001101100000110010101101","0010111101001011100001000100000101100111100010000","1001100111100100001000100000111010011100001011101","0111100001000001010100010100101100011011110010111","1110001000110100000011111010111110010101100110000","0011111111100111011101000111001001000001000010000","0010100101011101101001001010001010110001010000010","0100000000100000001011010110001110110011010000010","0000010101000101011100100000000010101101001011001","0111110010101010010101111101100001001010000100001","1101011111001100001011100111000100100001010010000","0111101110101110111110001101010101101100001010010","0001001101101000010111100000110000000100111000011","0100100111100011000111001001100101100100010011000","0000110001100000000010011010100000110011110010001","1001011001001100011010110000110110000100011110000","1111100000000000001110011110011001001100010000001","1010111010001101001101011001010011101100000010001","0000001010110010010111110111101100111110001101000","0100110000100001011000010000011000010100111000101","0000001011100111111011011011111000010010001100100","0010100000010110000010011010001010110110111100000","1001011010000100110101011100000101010100111010110","0001011000011001010101011000000110111010010011000","0010011010001000011010100000100011010001110110010","1001010110000011000000101011010101001101011100000","1010000111000110110001100101010011100000000101001","1110000000001101101110000011111001100010100000000","1011010000100000010011010011100100001000011000110","1100010100001100001001110100100001011111000100101","0001011001101010100010110100001100001001000000010","0110110110111001110001001100101011010100100100101","1000010100001100011000011111100100111010000111100","0010001011010001010000101011010100011010100100001","0001110111110110011000011110001111010000110000110","0000110000001010001000101011011000001001011101111","0110100101101110011000010000001110100011001010111","1000001000001001100111101001101010100100001101110","0111001010010010110001010100001110011000100111010","0000111001110001010101111011101011100010101001000","0011100000110011100000011110110000010100000001100"}

Returns: 777
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Returns: 15
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Returns: 477
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Returns: 797
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Returns: 7
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Returns: 1267
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Returns: 917
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Returns: 35
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Returns: 1571
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Returns: 19
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Returns: 2003
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Returns: 31
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Returns: 11
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Returns: 79
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Returns: 29
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Returns: 19
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Returns: 1481
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Returns: 39
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Returns: 1891
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Returns: 1087
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Returns: 63
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Returns: 303
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
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Returns: 0
{"111", "111", "100" }

Returns: 5
{"100", "000", "010", "000" }

Returns: 3

Statistics

Problem Statement for "LightbulbGame"

Problem Statement

Definition

Constraints

Examples