Four men, Eddie Jake, Deon, and Fred are watchmen in a small factory in Lorain. Their job consists of two daily shifts of six hours each, interrupted by a rest of several hours. At any hour of the day or night there must always be two men on duty. However, no two men's shifts may end at the same time, it is not wise for both people on duty to begin their shifts simultaneously. Each shift has to begin on the hour. Except for these rules, the four men may agree among themselves on any schedule they want.
So they have a meeting at which they ask for the following privileges: Jake wants to start his first shift at midnight and would like to be off for the day by 4 pm. Fred wants to relieve Deon after Deon's evening shift. Eddie has to be on the premises at 9 am to receive special instructions.
After some trial and error the four watchmen finally succeed at making out a shift schedule in accord with the regulations as well as their special wishes. What is the schedule?
Let's break down the given information step-by-step to construct the schedule:
1. Two shifts of six hours: This means that each watchman will have a shift of 6 hours, and there will be a rest period between the shifts.
2. At any hour, there must always be two men on duty: This means that there cannot be a time when only one watchman is on duty.
3. No two men's shifts may end at the same time: This means that the shifts must be staggered, and no two watchmen can finish their shifts simultaneously.
4. It is not wise for both people on duty to begin their shifts simultaneously: This means that the shifts should not start at the same time.
5. Jake wants to start his first shift at midnight and be off for the day by 4 pm: This means that Jake's first shift will start at midnight and end at 6 am, and he wants his second shift to end at 4 pm.
6. Fred wants to relieve Deon after Deon's evening shift: This means that Fred's first shift will start after Deon's evening shift and end at midnight.
7. Eddie has to be on the premises at 9 am to receive special instructions: This means that Eddie's first shift will start at 6 am and end at noon, and he wants his second shift to start at noon.
Now let's construct the schedule based on these requirements:
- Midnight to 6 am: Jake's first shift.
- 6 am to noon: Eddie's first shift.
- Noon to 6 pm: Deon's first shift.
- 6 pm to midnight: Fred's first shift.
Based on Fred's request to relieve Deon after his first shift, we can determine that Deon's second shift will start at 6 pm, which means Fred's second shift will start at midnight and end at 6 am.
Since Jake wants to be off by 4 pm, his second shift should start at 6 am and end at 4 pm.
Eddie needs to be on the premises at 9 am, so his second shift will start at noon and end at 6 pm.
Based on these adjustments, the final schedule is as follows:
- Midnight to 6 am: Jake's first shift.
- 6 am to noon: Eddie's first shift.
- Noon to 6 pm: Deon's first shift.
- 6 pm to midnight: Fred's first shift.
- 6 am to 4 pm: Jake's second shift.
- Noon to 6 pm: Eddie's second shift.
- 6 pm to midnight: Deon's second shift.
- Midnight to 6 am: Fred's second shift.
This schedule fulfills all the given requirements and regulations.
To find the schedule that satisfies the given conditions, we can follow these steps:
Step 1: Determine the possible starting times for each person's first shift.
According to the rules, each shift must start on the hour. Eddie needs to start at 9 am, so that's fixed. Jake wants to start at midnight, which is also an hour option. Fred wants to relieve Deon, so that means Fred's shift must start after Deon's shift ends. Since Deon could work the evening shift, the latest his shift could end is before midnight, which means Fred's shift can begin at midnight or later.
Step 2: Assign shifts to the watchmen based on their preferences and the rules.
We will consider the possible starting times for Fred's shift and find a suitable schedule.
Option 1: Fred starts at midnight
If Fred starts at midnight, Deon's shift needs to end before midnight. Based on this, we can assign the following shifts:
- Eddie: 9 am - 3 pm
- Jake: 3 pm - 9 pm
- Deon: 9 pm - 12 am (midnight)
- Fred: 12 am (midnight) - 6 am
Option 2: Fred starts after midnight
If Fred starts after midnight, he can start at 1 am or later. Let's consider the case where Fred starts at 1 am:
- Eddie: 9 am - 3 pm
- Jake: 3 pm - 9 pm
- Deon: 9 pm - 1 am
- Fred: 1 am - 7 am
Now, let's check if this schedule satisfies all the conditions:
- At any hour of the day or night, there must always be two men on duty. In both options, we have two watchmen working during every shift.
- No two men's shifts may end at the same time. In both options, the shifts end at different times.
- It is not wise for both people on duty to begin their shifts simultaneously. In both options, the shifts start at different times.
Therefore, both options satisfy all the given conditions. The shift schedule for the four watchmen could be either:
Option 1:
- Eddie: 9 am - 3 pm
- Jake: 3 pm - 9 pm
- Deon: 9 pm - 12 am (midnight)
- Fred: 12 am (midnight) - 6 am
Option 2:
- Eddie: 9 am - 3 pm
- Jake: 3 pm - 9 pm
- Deon: 9 pm - 1 am
- Fred: 1 am - 7 am