IBM Ponder This #182 · June 2013

Find a rational number (a fraction of two integers) that satisfies the following conditions:

1. Its denominator is five digits long and all of them are different.
2. In the infinite decimal representation, every digit occurs an equal number of times in the digits from one billion to two billion places to the right of the decimal point (inclusive), except for the last digit in the denominator, which occurs twice as often as the other nine digits.
3. Its numerator contains as few different digits as possible.

Update 6/4: To clarify the problem, here is an example: 5/17 = 0.294117647058823529411764705882... and in the 11 digit in the places 20-30 after the decimal point the digit 7 (the last digit of the demonimator) appears twice as many times as the digit 4, but not twice as many as the digit 9 (which does not appear there at all).

Solution

Best opened after a real attempt

To be added.