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This is correct. Each configuration can be described by two numbers (a, b) which say how much water is in the bigger and in the smaller glasses, respectively. The configuration space, i.e., all attainable configurations lie on the border of the X x Y rectangle . Indeed, we start with (0, 0), which is on the border. Also, after each move, one of the two smaller glasses is either full or empty (we pour until the recipient is full or the source is empty). This means that when X >= Y > 1, there are unattainable configurations. I'll leave it to you to confirm that when Y = 1, every configuration is attainable.I have tried different amounts for X and Y and have noticed that the attainable solutions are always on the boundary

Another way to see that there are unattainable configurations is to make X and Y even. Then one can show that each attainable configuration is expressed by even numbers.

There are several pages about this problem on the cut-the-knot site. This link describes the puzzle in graph-theoretic terms.