Logic Puzzle # 138 Logic Problems Help

Pinocchio's Nose
by Randall L. Whipkey

When Pinocchio arrives home late in the evening, his worried father Geppetto questions his beloved puppet boy as to what he has been doing, at one point, having smelled smoke on the little wooden head's clothing, asking if Pinocchio has been smoking a cigar. Pinocchio answers each question with a lie, of course--which causes his nose to grow a number of whole cm. (this is Italy). Pinocchio's five lies stretch his nose from its original 1 cm. to 35 cm., much to his, and his father's, dismay. From the tale of woe below, can you find the order in which Pinocchio tells his lies and how much his nose grows with each prevarication?

1. In consecutive order first-to-last, Pinocchio tells three lies: he says he is late because he was helping the Widow Marconi pull weeds from her garden; he tells a lie while trying to hold his nose back from growing; and he denies knowing who stole coins from Geppetto's shop, ashamed that he himself is the thief. Pinocchio's nose grows 3 cm. longer in telling the third lie than in telling the second of the three lies, and it grows three times as much from the third lie as from the first.
2. None of the five lies causes Pinocchio's nose to grow the 13 cm. that his all-time biggest lie, told the day before, causes.
3. When Pinocchio says he hasn't been with the bad boy Lampwick, his nose grows 6 cm., sprouting from 4 to 10 cm. in length.
4. When Geppetto asks his son if he attended school during the day and the puppet boy says yes, Pinocchio doesn't notice that his nose grows because it increases less than 4 cm. in length.

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