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This problem benefits from a systematic treatment.
Stretching Fractions
Age 14 to 16
Challenge Level 
This problem benefits from a systematic treatment.
Please see the Hint for useful categories when constructing a systematic approach.
The interest in this problem is the structure not simply the
results - where do the various start fractions go to and why?
An article that examines this problem in more depth can be
found here.
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