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Math Help - Fibonacci problem

  1. #1
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    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.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ljonz View Post
    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 N(n) denote the number of ways of inserting coints for n hours, then

    N(n)=N(n-1)+N(n-2)

    That is coins for parking n hours use a method of inserting coins for n-1 hours plus a \$1 coin, or a method of inserting the coins for n-2 hours floowed by a \$2 coin. The rest follows from your initial conditions.

    RonL
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