Math Is Fun Forum

iasonidis

Guest

Factory and workers

Guys, I have been given this problem more than a year ago but still struggling to solve it
Perhaps you can help me out! Here it is:
A large industrial site has 5000 workers. For each of them, the sum of his direct superiors and subordinates is 7.
Every day there are several work orders, for which the pattern of issuance, communication and execution is as follows, for every day of the week:
1. Every Monday, each worker issues a work order and distributes copies of it to his direct subordinates (if, of course, he has any - otherwise he executes them himself).
2. Each Tuesday, all workers 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 workers 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 (that is, any remaining work orders will be executed by the workers themselves). 
What is the MINIMUM number of workers that do NOT have direct superiors? Note that one worker may have shared subordinates with some other worker(s).