Which Alice?

ALICE IN PUZZLE-LAND
that if we multiply the number of acres in the original piece by 9/10,
we get the present piece—10 acres. So, to get from the present piece
back to the original piece, we must divide by 9/10! Now, to divide by
9/10 is to multiply by 10/9, so we multiply 10 by 10/9, getting 100/9,
which is 11 1/9 acres.
Does this check? Let us see: The original piece is 11 1/9 acres. Onetenth
of 11 1/9 is 1 1/9, so taking that away leaves exactly 10 acres.
ANOTHER ACREAGE PROBLEM Reducing everything to sixtieths,
1/3 + 1/4 + 1/5 = 20/60 + 15/60 + 12/60 = 47/60. This leaves
13/60 for the cultivation of corn. Therefore, 13/60 of the land is 26
acres, and since 13 is half of 26, then 60 must be half of the total
number of acres. So the land has 120 acres.
Let us check: One-third of 120 is 40, which is for the squash; onefourth
of 120 is 30, which is for the peas; and one-fifth of 120 is 24,
which is for the beans. Now 40 + 30 + 24 = 94, which leaves 26
acres for the corn.
THE CLOCK STRIKES TWELVE Between the first stroke and
the sixth stroke there are five intervals of time, and it takes thirty
seconds to cover those five intervals; so the interval between any two
consecutive strokes is six seconds (not five seconds, as some people
mistakenly conclude!). Now, between the first stroke and the
twelfth, there are eleven time intervals; so it takes the clock sixty-six
seconds.
THE TWELFTH QUESTION Suppose Alice had answered yes.
Then the Queen could fail her or pass her, as she pleased. If she
failed her, and Alice asked why, the Queen could say, "You got the
last question wrong—after all, you said you would pass and you
didn't—and since you got the last question wrong, you have to fail!"
168