Fairy Tale Mathematics

Pinocchio

Number Patterns

Pinocchio's nose grows longer each time he tells a lie. In the first version of the fairy tale, his nose grows by 5cm each time he lies. In the second version of the fairy tale, his nose doubles in length each time he lies. If his nose is 2cm long at the beginning of the story, how many lies would he need to tell for his nose to be approximately the same length in both versions of the fairy tale? How many lies would he need to tell in each version for his nose to be longer than one metre?

Problem from The Mathematical Association of Victoria 

Please email any attempts at the problem in whatever form they come to lmaidment@santglen.catholic.edu.au