There are 60 records given to you which correspond to a prisoner who is imprisoned for 60
^{ } days. He has 6 relatives one of whom visits him daily and the others visit him every i
^{th} day from the day of his imprisonment (i=2,3,4,5,6 for these 5 relatives).
Every record is sealed with the day number on it which indicates the number of days he is jailed when the record is filed with the names of visitors on that particular day. You have to make a new record which should be filled with the following details:
visitor name  number of visits after 60 days
Assume that no other relatives visited him at all, names of these 6 relatives are different and you don't know their names. Find the minimum number of records that need to be checked to make the new record correctly. Find the number of ways you can choose the minimum number of records and you can still make the new record correctly.
well so far the best I can come up with is 5 records.
Start with record 60, since this is a multiple of 1,2,3,4,5,6 all names will be on it
then open record 15, this will give you names 1,3,5 and by elimination from record 60 also give you 2,4,6
then open record 4, this will have names 1,2,4 but 1 will be the only name also on record 15 so will now have name for i=1
now open record 5, this gives 1 and 5, since we know 1 then we get 5 and by elimination from record 15 we also get 3.
finally open record 2 and this gives 1 and 5, since we know 1 then we get 2 and by elimination from record 4 we get 4.
So we now know all the names for i=1,2,3,4,5,6
and i=1 visits 60 times
i=2 visits 30 times
i=3 visits 20 times
i=4 visits 15 times
i=5 visits 12 times
i=6 visits 10 times
As for how many different ways this can be done, I'm currently working on that. I'm doubting it can be done with fewer records but I could be wrong :)

Posted by Daniel
on 20090121 15:52:15 