Thread: Fibonacci problem

You are parking your car, and the meter takes only 1 and 2 dollar coins/notes. For 1 hour, there is only one way to insert the coins= 1of $1. For 2 hours, there are 2= $1+ $1 and $2. For 3 hours, there are three ways= $1 +$1+ $1, $1+$2, and $2+$1. Show the formula proving that the number of ways to insert coins for hours forms a fibonacci sequence.

Originally Posted by ljonz

You are parking your car, and the meter takes only 1 and 2 dollar coins/notes. For 1 hour, there is only one way to insert the coins= 1of $1. For 2 hours, there are 2= $1+ $1 and $2. For 3 hours, there are three ways= $1 +$1+ $1, $1+$2, and $2+$1. Show the formula proving that the number of ways to insert coins for hours forms a fibonacci sequence.

Let denote the number of ways of inserting coints for hours, then



That is coins for parking hours use a method of inserting coins for hours plus a coin, or a method of inserting the coins for hours floowed by a coin. The rest follows from your initial conditions.

RonL