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Sunday Times Teaser 2664 – Time ‘n’ Again

by Victor Bryant

The following sum involves the conversion of a fraction in its simplest form into a recurring decimal:

TIME
——–      =   .AGAINAGAIN …
**N**

where letters consistently represent different digits and asterisks (*) represent any digit.

Numerically, what is TIME?

5 Comments Leave one →
  1. brian gladman permalink

    • brian gladman permalink

      Another version that is much faster along the lines of Arthur’s below:

  2. Similar analysis to Brian, using the factorisation of 99999=3^2*41*271, but using the equation

    3^2*41*271 * TIME = AGAIN * xxNxx, and distributing the factors of 99999 amongst AGAIN and xxNxx

  3. And a faster version, using Brian’s observation that **N** has to be 11111 or 33333

    • brian gladman permalink

      Hi Arthur

      I hope you don’t mind but I have deleted the incorrect version and, while I was at it, I converted your corrected version to Python 3 (I get emails telling me that some code here doesn’t work and I often find that this is because people are using Python 3 without even realising that there is a Python 2).

      We seem to have converged on very similar solutions 🙂

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