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jmprada
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A large multi-national firm has 5000 employees. For each of them, the sum of his direct superiors and subordinates is 7.
The pattern of issuance, communication and execution of work orders for each week is as follows:
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?
The pattern of issuance, communication and execution of work orders for each week is as follows:
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?