I figured out the number one in about 30 seconds. The biggest clue is that it claims preschoolers get it easily. That means all mathematical operations, except addition and less likely subtraction, is out of the question. A quick glance showed that adding or subtracting in any simple way would not yield a result - a more complicated way would not be done by a preschooler. So that meant it probably was some sort of spacial or visual problem. Seeing 6666=4 and 0000=4 got me thinking about the shapes of the numbers, and from there I quickly determined the answer was the number of closed loops.