Even after repeated request for explanation for the question LEPAINTS in July long challenge, no explanation is being provided for any of the test cases. Its not like hint is being asked, expanation will only make question more clearer to larger no. of audience and will greatly help newbies to try n solve the question. Please do not force us to think that explanation is deliberately being avoided.
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The problem here is that the samples are too large for any clear and short explanation. Even the smaller one with 4 re-paintings has 3^4=81 ways to pick the colours, and that’s not even talking about the subsets.
Besides, the statement’s pretty clear as it is.
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Maybe a case should be given which can also be solved manually.
Otherwise, even if someone provides some more data of the given sample eg: answer after each ‘turn’, then also the question will become clearer.
Otherwise, please provide an additional and simpler ‘test case’ for explanation.
I am getting 3.4783 and 22.1933 … as the sample answers which are close to the actual answers. 
The problem is if you explain it properly you will get the answer itself.
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One clarification please-
Is the subset mentioned in the problem a continuous subset in the range [L,R]( [l,r] in [L,R]) or is it a random selection from all elements in range [L,R]( {ai} for random i’s in [L,R])
random selection as mentioned in the problem statement…
Thanks 
even if nobody can explain the test case…can anybody explain the number of cases that will be formed int the first test case…
my doubt is that while considering an empty subset do we still consider all the colors…??
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@vikram yes we have to. Although instead of asking you could have tried it both ways .
Even I had the same doubt.
because i tried both the ways on sample tests and only got correct answer for the one which i have mentioned.
i have not solved the problem yet, i have only figured out the combinatorial part. i have yet to take care of handling of the huge numbers involved.
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