As it happens, I'm still not sure if I was in error. Here's an alternative argument: the hotter water should first cool down to 20°, and then do whatever the 20° water does to freeze. So, the hotter water takes a little more time to freeze than the colder water.
As pointed out in this paper, which surveys the problem and discusses its ramifications on the thinking and doing of physics, the error in this last argument is that it implicitly assumes that temperature is the sole factor that determines the rate of freezing.
The problem is a long-standing one. Aristotle had this to say:
If water has been previously heated, this contributes to the rapidity with which it freezes: for it cools more quickly. (Thus so many people when they want to cool water quickly first stand it in the sun: and the inhabitants of Pontus when they encamp on the ice to fish. . . pour hot water on their rods because it freezes quicker, using the ice like solder to fix their rods.) And water that condenses in the air in warm districts and seasons gets hot quickly.
Some will say that a car should not be washed with hot water because the water will freeze on it more quickly than cold water will, or that a skating rink should be flooded with hot water because it will freeze more quickly.
1. Monwhea Jeng, Hot water can freeze faster than cold?!? Am. J. Phys. 74, 514 (2006).