how many operation , you will perform?? [closed]

You have n friends having some marbles initialy let ith friend has Mi marbles.you have infinite number of marbles. and you can perform folowing operation to equalize the marbles among your friends

1.you chose a friend , and give the others one marble except to chosen on.

2.you chose a friend , and give the others two marble except to chosen on.

3.you chose a friend , and give the others five marble except to chosen on.

tell minimum number of time you have to perform the above operations to equalize the marbles??plz help i realy can not get the right touch to such type questions.

example- let n=3 and initial marbles are

3 2 5

chosing 5

operate operation 2 (incresing others by two except chosen one 5)

5 4 5

chosing 5

operate opration 1 (incresing others by one except chosen one 6)

6 5 5

now chosing 6

operate opration 1 (incresing others by one except chosen one 6)

6 6 6

so minmum number of operations are three.

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Forget about minimum, can you prove that some solution always exists? –  vadim123 Jun 1 '13 at 3:47
ther will be always a solution due to operation 1.....but it is not the problem –  kumar Jun 1 '13 at 3:53
How do you know it will always be possible? Your proof of this is the key to answering the original question. –  vadim123 Jun 1 '13 at 4:05
@ vadim it is constantly possible to encrease no frnds with equel marbles... thtz y m thinking... can you plz make it more clear??? –  kumar Jun 1 '13 at 4:09
This question is very similar to math.stackexchange.com/questions/408042/… except that one is taking away rather than adding –  Mark Bennet Jun 1 '13 at 6:55
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closed as not constructive by Andres Caicedo, Amzoti, Stahl, Mark Bennet, Ｊ. Ｍ.Jun 1 '13 at 18:06

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