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Project Euler Solutions

Project Euler 104 Solution

Project Euler 104 Solution

Project Euler 104: Find the first Fibonacci number for which the ends are pandigital.


Problem Description

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.

It turns out that F541, which contains 113 digits, is the first Fibonacci number for which the last nine digits are 1-9 pandigital (contain all the digits 1 to 9, but not necessarily in order). And F2749, which contains 575 digits, is the first Fibonacci number for which the first nine digits are 1-9 pandigital.

Given that Fk is the first Fibonacci number for which the first nine digits AND the last nine digits are 1-9 pandigital, find k.

Analysis

Even calculating the Fibonacci sequence without any optimization this solution was lightning fast. Getting the bottom 9 digits was easy and has been done in previous problems. The top 9 required the formula:

phi = (1 + sqrt(5)) / 2
t = n * log10(phi) + log10(1/sqrt(5))
t = int((pow(10, t – int(t) + 8)))

So, after finding a candidate with the bottom 9 digits pandigital we query the formula to see if the top 9 are pandigital. The first one found will be our first solution.

Project Euler 104 Solution

Runs < 0.050 seconds in Python 2.7.

download arrowUse this link to get the Project Euler 104 Solution Python 2.7 source.

Afterthoughts

Project Euler 104 Solution last updated

Discussion

3 Responses to “Project Euler 104 Solution”

  1. sorry but 329468 is not the solution 🙂

    Posted by diego | September 10, 2011, 9:52 PM
  2. Can you explain how t gets the top 9 digits?

    Posted by Daniel | October 19, 2009, 7:58 PM

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