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Logic Puzzle # 138 Logic Problems Help



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 (1-4 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 3X-3 cm. Summing, 7-3 = 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



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