The won function for fifteen is driving me crazy! Here's my implementation. I've run it through debug50 and it appears to work as expected. However, check50 only passes on a 4x4 board, but not a 3x3. Can someone help me spot the error in my code?

bool won(void)
    int counter1 = 0;
    int counterr = 0;
    int counterc = 0;

    for (int row = 0; row < d; row++)
        for (int column = 0; column < d; column++)

            if(counterc == d)
                counterc = 0;

            if (board[row][column] < board[counterr][counterc])
    if (counter1 == d * d - 2) // The minus 1 is to account for the 0 at the end
        return true;

        return false;

2 Answers 2


I suspect that a 4x4 can also generate false wins, given the right sequence of inputs.

The problem is that the won() function, as written, can report a win when the tiles are in a certain order. If the blank tile is out of place but the remaining tiles are in sequential order, it will result in a win being reported.

A simple fix would be to check that the 0 tile is in the correct location. In fact, doing this first will significantly increase the efficiency of the won function because most of the time, the 0 tile is out of place. If it is out of place, there's no reason to check anything else.

You might also increase efficiency by comparing each tile against a counter instead of the next tile.

If this answers your question, please click on the check mark to accept. Let's keep up on forum maintenance. ;-)

  • Many thanks! I rewrote my code to check if 0 was in the bottom right corner, and compared the array to a counter, as you suggested. It now works perfectly. Thanks again for your help!
    – Jason_V
    Jun 7, 2017 at 21:48

A possible pseudocode for win would be:

for row
    for column
        // in each movement, if the position of board [i] [j] coincides with  
        //  the expected value increases
        // the counter in 1 if some value differs from the expected we left won
        if board[i][j] == expected value
          return false

        // if at the end of the loop count matches the number of tiles, we are 
        //in the winning configuration  
       if count == d*d -1
       return true 

The trick is expected value, there is a simple arithmetic relationship between i, j and d that gives us such relationship for example in the winning configuration:

board[0][0] = 1
board[0][1] = 2

etc... I let you find this relationship

  • Yes, but did you figure out what was wrong with his code, MARS? ;-)
    – Cliff B
    Jun 7, 2017 at 21:33

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