A large company has a phone tree to contact its employees in case of an emergency factory shutdown. Each of the five senior managers calls three eployees, who calls three other employees and so on. If the tree consists of seven levels, how many employees does the company have?
To find the number of employees in the company, we need to calculate the total number of nodes in the phone tree.
Since the phone tree has seven levels, we can start by determining the number of nodes at each level:
- Level 1 (top level): 1 node (the CEO or highest-ranking manager)
- Level 2: 3 nodes (each senior manager is called by the CEO)
- Level 3: 3 * 3 = 9 nodes (each of the 3 senior managers calls 3 employees)
- Level 4: 3 * 3 * 3 = 27 nodes (each employee from Level 3 calls 3 employees)
- Level 5: 3 * 3 * 3 * 3 = 81 nodes
- Level 6: 3 * 3 * 3 * 3 * 3 = 243 nodes
- Level 7 (bottom level): 3 * 3 * 3 * 3 * 3 * 3 = 729 nodes
To find the total number of employees, we sum up the nodes at each level:
1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093
Therefore, the company has a total of 1093 employees.