About a multi-national company

[chen.aavaz]

Dear all,
I would really appreciate if you could help me with the below problem:
I have not been able to figure any solution so far!
"A large multi-national firm has 5000 employees. For each of them, the sum of his direct superiors and subordinates is 7.
Below is the pattern of issuance, communication and execution of work orders for each week:
1. Every Monday, each employee issues a work order and distributes copies of it to his direct subordinates (if, of course, he has any).
2. Each Tuesday, all employees that received work orders on Monday, distribute them to their direct subordinates, if any; otherwise they execute them themselves.
3. Each Wednesday, procedure number 2 is repeated: any employees that received work orders on Tuesday, distribute them to their subordinates, otherwise they execute them themselves. Same also on Thursday and Friday.
Finally, on Friday there are no more work orders for distribution to any subordinates.
What is the MINIMUM number of employees that do NOT have direct superiors? Note that some superiors may have common subordinates (shared)."

 

[Deleted member 4993]

Dear all,
I would really appreciate if you could help me with the below problem:
I have not been able to figure any solution so far!
"A large multi-national firm has 5000 employees. For each of them, the sum of his direct superiors and subordinates is 7.
Below is the pattern of issuance, communication and execution of work orders for each week:
1. Every Monday, each employee issues a work order and distributes copies of it to his direct subordinates (if, of course, he has any).
2. Each Tuesday, all employees that received work orders on Monday, distribute them to their direct subordinates, if any; otherwise they execute them themselves.
3. Each Wednesday, procedure number 2 is repeated: any employees that received work orders on Tuesday, distribute them to their subordinates, otherwise they execute them themselves. Same also on Thursday and Friday.
Finally, on Friday there are no more work orders for distribution to any subordinates.
What is the MINIMUM number of employees that do NOT have direct superiors? Note that some superiors may have common subordinates (shared)."

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[chen.aavaz]

Just some thoughts

I am really stuck at the beginning...
Let the number of employees that do not have direct superiors be n.
Now, number of total direct subordinates of n employees are 7n,
Therefore, number of direct subordinates of 7n is 6 * 7n (since each have a
direct superior already, so 7-1 ) and so on. Then all these total to 5000 and this seems to be a geometric series.
But I am confused by the note that "some superiors may have common subordinates (shared)"