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UKMT Mathematical Olympiad for Girls, 2014

Combinatorics Difficulty 1.0 Junior Prove it United Kingdom

Call a number 'hexed' when it has a recurring decimal form in which both the following conditions are true.

(i) The shortest recurring block has length six.
(ii) The shortest recurring block starts immediately after the decimal point.

For example, $987.\dot{1}23\,45\dot{6}$ is a hexed number (the dots indicate that $123\,456$ is a recurring block).

How many hexed numbers are there between 0 and 1?

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