Which Alice?

ALICE IN PUZZLE-LAND
WHO IS OLDER? We must first determine how many days it
will take for the two watches to be together again. Since the March
Hare's watch loses time at the same rate as the Hatter's watch gains,
then the next time the watches will be together again is when the
Hatter's watch has gained six hours and the March Hare's watch has
lost six hours. (Then both watches will read six o'clock, and, of
course, both watches will be wrong.) Now, how many days will it
take for the Hatter's watch to gain six hours? Well, a gain of 10
seconds an hour is one minute in six hours, which is 4 minutes a
day, which is one hour in 15 days, which is 6 hours in 90 days. So in
90 days the watches will be together again.
Now, we were not told on what day in January the two watches
were set right. If it were any day other than January 1, 90 days later
couldn't possibly fall in March; it would have to fall in April (or
possibly May). So the watches must have been set right on January
1. But even then, 90 days later couldn't fall on any day in March
unless it's leap year! (The reader can check this with a calendar.
Ninety days after January 1 is April 1 on an ordinary year, and
March 31 on a leap year.) This proves that the March Hare's
twenty-first birthday falls in a leap year, hence he must have been
born in 1843, rather than 1842 or 1844. (Twenty-one years after
1843 is 1864, which is a leap year.) We are given that one of the two
was born in 1842, hence it was the Hatter who was born in 1842. So
the Hatter is older than the March Hare.
Chapter 5
ENTER THE FIRST SPY C certainly cannot be a knight,
because no knight would lie and claim to be the spy. Therefore, C is
either a knave or the spy. Suppose C were the spy. Then A's claim is
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