Logic Problem Solution:
Pinocchio's Nose
By clue 1, Pinocchio tells three consecutive lies as follows: first, he tells Geppetto that
he is late because he helped the Widow Marconi pull weeds; second, he tells another lie; and
third, he tells his father he hasn't stolen any coins from the shop till. Also by clue 1,
Pinocchio's nose grows 3 cm. more on the third lie than on the second and grows 3 times as
much on the third lie as on the first. By clue 3, Pinocchio's lie that he hasn't been
with Lampwick causes his nose to grow from 4 cm. to 10 cm. in length. If Pinocchio tells
that lie as the second lie in clue 1 and his nose grows 6 cm., the third lie would
cause a 9 cm. lengthening and the first lie a 3 cm. increase in the size of his nose.
From the introduction, the five lies cause Pinocchio's nose to grow 34 cm., from its
normal length of 1 cm. to a whopping 35 cm. Adding the three lengths if clue 3 were an
overlap with clue 1, Pinocchio's nose would grow 18 cm., leaving 16 cm. for the
other two lies. Since Pinocchio's nose grows 3 cm. or less when he tells Geppetto he
attended school (clue 4), the fifth lie would spur a 13 cm. or more burst in nose size,
contradicting clue 2. So, the clue 3 lie that he hasn't been with Lampwick is the fourth one
to the three in clue 1. The three in clue 1 can't precede the lie in clue 3, since the
total growth in clue 1 has to be more than 3 cm., the maximum size growth (14 cm.) if
the lie in clue 3 were after the lies in clue 1. The lie in clue 3 about being with Lampwick
must be the second one Pinocchio tells, with the first lie then causing his nose to grow
3 cm., going from 1 to 4 cm. in length. The three lies in clue 1 then cause Pinocchio's
nose to grow 25 cm., going from 10 (3) to 35 (introduction) cm. in length. Letting
the third lie, the one in clue 1 about being late, equal X in nose growth, the
fifth lie, about stealing money, causes 3X in elongation, and the fourth lie grows
the nose 3X3 cm. Summing, 73 = 25, so = 4. The third lie about his
lateness causes Pinocchio's nose to grow 4 cm., the fifth lie about his theft causes his
nose to lengthen 12 cm., and the fourth lie results in an extra 9 cm. of nose. The fourth
lie can't be the one about attending school (4), which then must be the first lie Pinocchio
tells. The fourth lie is that he hasn't smoked a cigar. In sum, Pinocchio tells lies to
Geppetto as follows:
 1  4 cm. (3 cm.)  Attended school
 4 10 cm. (6 cm.)  Hasn't met Lampwick
 10 14 cm. (4 cm.)  Is late because he helped the Widow
 14 23 cm. (9 cm.)  Hasn't smoked a cigar
 23 35 cm. (12 cm.)  Hasn't stolen money

