Which Alice?

ALICE IN PUZZLE-LAND
the same as it is now—namely 29 years. So when the prisoner is 29,
the gaoler will be twice as old (58). So the prisoner has to wait 4
years.
HOW LONG TO GET OUT? The answer is not 30 days; the
frog could get out on the evening of the 28th day. On the
morning of the 2nd day, the frog will be one foot from the
bottom; on the morning of the 3rd day he will be 2 feet from the
bottom—and so forth until the morning of the 28th day, when he
will be 27 feet from the bottom. On the evening of that day he will
have reached the top, and so will not have to slide back again.
DID HE CATCH THE TRAIN? The cyclist made the mistake of
averaging over distances rather than times! If he had spent equal
times going four miles an hour, eight miles an hour, and twelve
miles an hour, he would indeed have averaged eight miles an hour,
but he spent most of his time going uphill and least of his time
going downhill.
It is easy to calculate how long the trip took him: He spent one
hour going uphill, a half-hour—or thirty minutes—going on level
ground, and one-third of an hour—or twenty minutes—going
downhill. This adds up to an hour and fifty minutes, so he missed
the train by twenty minutes.
WHAT ABOUT THIS ONE? When the man arrived at the first
station, the train had left a minute earlier. Ten miles an hour is one
mile in 6 minutes, or 1 1/2 miles in 9 minutes. So the train reached
the second station 8 minutes after the man arrived at the first
station. The train waits 14 1/2 minutes at the second station, so the
man has 22 1/2 minutes to catch the train at the second station.
Four
154