Which Alice?

Solutions to the Puzzles
same number as Tweedledee), so he now has one more than half
the total. If he wins the bet, then he will have two more than half
the total. Also, he will then have two-thirds of the total (which is the
same thing as having twice as many as Tweedledee), which is onesixth
of the total more than half the total (because the difference
between one-half and one-third is one-sixth). Therefore, one-sixth
of the total more than half the total is the same thing as two more
than half the total, so two rattles is the same thing as half the total.
Therefore, the total number of rattles is twelve, so Tweedledum has
seven and Tweedledee has five.
Let us check: If Tweedledum loses, each will have six; if
Tweedledum wins, he will have eight and Tweedledee will have
four, so he will have twice as many as Tweedledee.
HOW MANY BROTHERS AND SISTERS? There are four boys
and three girls in the family. Tony has three brothers and three
sisters; Alice has four brothers and two sisters.
HOW MANY WERE WRONG? Exactly three right is the same
thing as exactly one wrong, so the choice is between exactly three
right and exactly two right. Now, it is impossible to get exactly three
right, because if three are right, the fourth must also be right!
Therefore, she got exactly two right.
HOW MUCH LAND? A common wrong answer is 11 acres. If
there had really been 11 acres, the tax collector would have taken
away 1 1/10 acres (which is one-tenth of 11 acres), which would
have left the farmer with 9 9/10 acres rather than 10 acres, so 11
acres cannot be the right answer.
How does one find the right answer? Well, look at it this way:
After one-tenth of the farmer's land had been taken away, he had
nine-tenths left. So 9/10 of the original piece is 10 acres. This means
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