Geometric prices

Number Theory Level 4

Bob will buy a book if and only if:

  1. The price of the book is an integer number of cents, and ranges from \($1.00\) to \($9.99\), inclusive.

  2. The three digits in the price of the book in order form a geometric progression with a positive common ratio.

If Bob goes to a store with a single book of every possible monetary value, how many books will he buy?

Details and assumptions

For example, Bob will buy a book with price \($1.24\), but not one with price \($3.00\).


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