Project Euler 26 Mystery Cache

Acknowledgements

This cache was inspired by Project Euler.

General notes

• To solve Project Euler puzzles, you will probably have to write a computer program.
• Many of the containers are small, and contain neither pen nor pencil.
• There are explicit finding notes in each geochecker.

Reciprocal cycles

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2	=	0.5
1/3	=	0.(3)
1/4	=	0.25
1/5	=	0.2
1/6	=	0.1(6)
1/7	=	0.(142857)
1/8	=	0.125
1/9	=	0.(1)
1/10	=	0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that ¹/₇ has a 6-digit recurring cycle, and the four-digit sequence starting at the third digit is 2,8,5,7.

The Puzzle

Find the value of d < 10,000 for which ¹/_d contains the longest recurring cycle in its decimal fraction part.

At the 1,000^th digit in the decimal fraction you can find the sequence 0,2,4,5. To find this geocache first find the four-digit sequences starting at the 6,267^th and 4,456^th digits.