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Mahesh Abnave (Mahesha999)
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Learner and a well wisher
Learner and a well wisher

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I am trying to find:
Number of ways to distribute n "distinguishable" items to r "indistinguishable" cells when "repetitions allowed" and each cells receives "exactly one" item.

Distribution of n "distinguishable" items to r "distinguishable" cells when repetitions are allowed and each cell receives exactly one item is n^r. But I am finding it difficult what it will be for "indistinguishable" cells. Also no books talks about it!!!

I tried to enumerate small examples to come up with some series if not with some closed formula.

Let us consider n=7 and r=5.
When number contains single number:
11111,22222,33333,44444,55555,66666,77777 (clearly there are 7C1 such numbers in total)

When number contains only two numbers (which can be selected in 7C2 ways), say 1 and 2:
12111,12112,12122,12222
Trimming first two digits in each, we get 111,112,122,222
That is "distributing 2 distinguishable numbers in 3 indistinguishable cells with repetitions allowed and each cell receive exactly one number and each number appears zero or more times."

When number contains three numbers (which can be selected in 7C3 ways), say 1,2 and 3:
12311,12312,12313,12322,12323,12333
Trimming first three digits in each, we get 11,12,13,22,23,33
That is "distributing 3 distinguishable numbers in 2 indistinguishable cells with repetitions allowed and each cell receive exactly one number and each number appears zero or more times."
Also this gives feeling of inclusion-exclusion. Does this lead to Stirling number of second kind in some way?

We continue this till each number contains 7 numbers in which case there will be only 1 such number (as cells are indistinguishable/arrangement does not matters).

I am unable to generalize this in order to come up with some series if not closed formula.

Can anyone help or at least give some comment/hint? Does above makes sense?

I am trying to find:
Number of ways to distribute n "distinguishable" items to r "indistinguishable" cells when "repetitions allowed" and each cells receives "exactly one" item.

Distribution of n "distinguishable" items to r "distinguishable" cells when repetitions are allowed and each cell receives exactly one item is n^r. But I am finding it difficult what it will be for "indistinguishable" cells. Also no books talks about it!!!

I tried to enumerate small examples to come up with some series if not with some closed formula.

Let us consider n=7 and r=5.
When number contains single number:
11111,22222,33333,44444,55555,66666,77777 (clearly there are 7C1 such numbers in total)

When number contains only two numbers (which can be selected in 7C2 ways), say 1 and 2:
12111,12112,12122,12222
Trimming first two digits in each, we get 111,112,122,222
That is "distributing 2 distinguishable numbers in 3 indistinguishable cells with repetitions allowed and each cell receive exactly one number and each number appears zero or more times."

When number contains three numbers (which can be selected in 7C3 ways), say 1,2 and 3:
12311,12312,12313,12322,12323,12333
Trimming first three digits in each, we get 11,12,13,22,23,33
That is "distributing 3 distinguishable numbers in 2 indistinguishable cells with repetitions allowed and each cell receive exactly one number and each number appears zero or more times."
Also this gives feeling of inclusion-exclusion. Does this lead to Stirling number of second kind in some way?

We continue this till each number contains 7 numbers in which case there will be only 1 such number (as cells are indistinguishable/arrangement does not matters).

I am unable to generalize this in order to come up with some series if not closed formula.

Can anyone help or at least give some comment/hint? Does above makes sense?

Post has attachment
Smart Lockscreen Protector hides even pattern unlock screen (shows up blank screen instead) on Nexus 6 completely disabling to unlock the phone. I somehow unlocked it by turning on camera with long pressing volume button (I guess) and then getting to pattern unlock screen. Then I locked phone again to check if I can repeat the same. Nope I was not able to repeat. So somehow I power off the phone by long pressing power button. In short not able to use this app on Nexus 6. Sad.

Here are the videos:
https://www.youtube.com/watch?v=cbZdnCvuhUM
https://www.youtube.com/watch?v=F_HHAeYr-o4

Hi I was in love with the app. But now I see most of the files got stuck in the Conflicts!!! any advice? I really want to know why is this happening. I created a file on Desktop. Manually synced to Android folder using FolderSync. Now I opened it on Android, modified it and saved it. Now I opened the same file on Desktop. It opened old content. So modifying old content on Desktop and saving it. Will cause conflict right? Is Instant Sync only option here? (Also I have selected WiFi only sync. So Instant Sync will not happen unless I am in WiFi.)

What happens if I rename file on Desktop. Does the same file gets new name on mobile too?

Is instant sync supposed to eat a lot battery? I feel it does so. Need confirmation.

Feature Request
------------------------------------------
Set sync only on WiFi (auto turn on), instantly, and also every 15 minutes. Whenever I check status, it's almost always red. This is mostly when I am out of home on mobile data where FolderSync does not find WiFi. I guess there should be last successful sync time in folder pairs screen.

Is OneDrive sync working? What are all those "File Size Errors" ??? Does anyone else getting the same?

Post has shared content
Mozilla Introduces the Most Customizable Firefox Ever with an Elegant New Design - https://blog.mozilla.org/blog/2014/04/29/mozilla-introduces-the-most-customizable-firefox-ever-with-an-elegant-new-design/

What do you think about new design?
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Just blogged all about nasty this keyword in JavaScript
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