As this question makes clear, "which" is used when there is a set number of choices available, while "what" is used when there is not a set number of choices available.
Which term do we use, however, when we are referring to continuous numbers as opposed to discrete numbers? How about numbers that are technically continuous but are in practice discrete?
Discrete number example: Which parking spot were you assigned to? (There are a discrete set of parking spots which one could be assigned to).
Continuous number example: Which/what temperature do you brew your beer at? (There are an infinite amount of temperatures available; however, brewers typically brew between the ranges of 40*F and 85*F, so it would seem to be discrete. On the other hand, there are an infinite amount of numbers between two consecutive integers, i.e 41.1, 41.2, 41.22, 41.3333 ...)
When referring to time, which is another example of continuous or discrete (there are 24 hours in a day, but an infinite number of units in between two consecutive hours), I always hear people use "what"-- "What time is it? What time shall I pick you up?"
Answer
'What' is usually used for continuous data treated as, or rather being considered as, continuous: 'what time is it?' / 'what temperature do you brew your beer at?' / 'what speed are you doing?'
For days and years, both 'what day/year was that?' and 'which day/year was that?' are used. Time is continuous, but is often treated as if it were discrete, and is probably then being considered as discrete. This gets even more complicated, as you point out, because age in years is almost always treated as being (and is often thought of as being) discrete, but 'what age is he?' would be used.
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