Fraction and Unit Fractions.

May be this is the "help":

Guess you would have to write some routines to try "all" possibilities.

Using a generic brute force program I wrote some time ago I found some solutions for your first two problems.

Solutions with the smallest possible integers are

but if you allow bigger integers you get a lot more solutions. Below are the solutions for task 1 with integers from 1 to 200 and task to for the range 1 to 100.

As for the third problem, the denominator 2011 is a prime and so without amore intelligent algorithm we would have to try all numbers from 1 to 2011 at least. Probably there would be no solution found and we should try up to integer multiples of 2011. Trying all numbers from 1 to 2011 would mean we have to try 4^2011=5*10^29 times. Based on the timing with a smaller range this would take on my machine about 10^18 years!!

So problem 3 would require more thinking and less brute force.

Addendum: Here is one (of sure many) solution for your third problem, found by a different method, of course

Thats my second post after PTC introduced its "moderation" of all posts. The first was sent 6 hours ago and still is not open for public. Could image that if that kind of moderation stays, that I will go.