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As some people have noticed, sometimes the timer will not stop on one-click boards, even though only mine cells remain. Therefore, these boards seem impossible to finish. (However, they can be finished by right-clicking on any mine, as I've discovered.) By examining some of these boards, I noticed that every one I saw had a mine in the top left hand corner. I also know that if your first click is a mine, the mine is moved to the top left hand corner. Thus, I figured the timer does not stop on one-click boards if your first click was a mine. Now, I will try to prove that theory, by editing the winmine.ini to create custom boards that aren't normally possible...
First, we set a beginner board to contain 63 mines (only 1 non-mine square). Theoretically, since your first click can never be a mine, then every board should be a 1-second winner. But, if my previous hypothesis is correct, then only once in 64 tries should the timer actually stop right away. (It should actually stop when you click on the non-mine square. For the other 63 times, the timer shouldn't stop because you clicked on a mine on your first click, and it had to be moved.)
So, I set up this board and ran 100 tests...
2 times:
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| 17 times:
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Only 2 times did the board actually finish itself in one click like it should. 81 times the board displayed an 
with the timer still running. The remaining 17 times, the board wouldn't even allow me to open the cell. The "button depressed" picture remained, even when I let go of the mouse button. (But the cell still wasn't pressed - I could return it to its original unpressed state by clicking and dragging over top of it.) Hmmmm... this board is acting just like an all-mine board where the mine cannot be moved anywhere as there is no place to put it. But there are only 63 mines on this board; there should be space to move the mine somewhere! After some looking around on one of these 17 boards, I found the only square without a mine. In each one of these boards, the only non-mine square was either on the bottom edge or the right edge. Thus, I concluded that when your first click is on a mine, the program tries to move the mine to another space, but it doesn't check the right-most column or the bottom row. Why doesn't it? Probably a programming oversight, but then again, in normal boards the program should always be able to find a place for the mine without checking the right/bottom of the board. Thus, the fact that a mine cannot be moved to the right/bottom of the board is rather trivial, but still interesting nonetheless. I have also confirmed this behaviour in Intermediate and Expert.
So, have I "proved" anything with these results? Of course it isn't completely "solid" proof, but still, the results are close to what would be expected. (Taking into account the new glitch that a mine cannot be moved to the right/bottom.) The probability that you click on the one non-mine square is 1/64. The probability that the non-mine square is on the right/bottom edge is 15/64. The expected results would be: 1.56 times the board finishes itself, 75 times the appears and the timer keeps running, and 23.46 times the mine cannot be moved. (Assuming your click is in the middle of the board - if you click on the right/bottom edge, you are slightly less likely to get a board where the mine cannot be moved.) Anyway, for now it's proof enough for me. Of course, if you ever come across a 1-click board that doesn't stop the timer, and it doesn't have mine in the top left hand corner, then you've just ruined my whole theory.
