It’s the critical path Late and early start times stuff. With the middle numbers in between being the float 

Thank you for clarifying that the puzzle involves Critical Path Method (CPM) calculations, focusing on Early Start (ES), Late Start (LS), and Float (Slack) times. Let's go through the steps to correctly determine these values.

### Critical Path Method Overview:
1. **Early Start (ES) and Early Finish (EF)**:
   - **ES**: The earliest time an activity can start, given that all preceding activities are completed as early as possible.
   - **EF**: The earliest time an activity can finish, calculated as \( EF = ES + \text{Duration} \).

2. **Late Start (LS) and Late Finish (LF)**:
   - **LF**: The latest time an activity can finish without delaying the project.
   - **LS**: The latest time an activity can start without delaying the project, calculated as \( LS = LF - \text{Duration} \).

3. **Float (Slack)**:
   - The amount of time that an activity can be delayed without affecting the overall project timeline. Calculated as:
     \[
     \text{Float} = LS - ES = LF - EF
     \]

### Steps to Solve the Puzzle:
1. **Identify the Critical Path**:
   - The critical path is the sequence of activities that determine the project's shortest possible duration. Activities on the critical path have a Float of 0.

2. **Calculate ES and EF**:
   - Start with the first activity and set ES = 0. Move forward through the network, calculating ES and EF for each activity.

3. **Calculate LF and LS**:
   - Begin from the last activity, setting its LF equal to the project's required completion time. Move backward through the network to calculate LF and LS.

4. **Determine Float**:
   - Calculate the float for each activity. Activities with a Float of 0 are on the critical path.

### Analysis of the Provided Puzzle:
1. **Top-Left Grid (Start Node)**:
   - This likely represents the starting point with ES = 0. Calculate EF based on the activity duration.

2. **Middle Grids**:
   - For each connected grid, calculate ES and EF moving forward. Once the end is reached, calculate LF and LS moving backward.

3. **End Grids (Finish Nodes)**:
   - The final grids should give you the total project duration.

### Correcting Mistakes:
- **Check each connection**: Ensure that the ES of a subsequent activity is equal to the EF of its predecessor.
- **Critical Path**: Identify where the float is zero and ensure these activities align with the project's shortest duration.

Would you like to go step-by-step through the calculation process for each grid? 

Here are 5 questions that may help solidify the understanding:
1. What are the ES and EF values for the first activity in your diagram?
2. How do you ensure the float is calculated correctly between each activity?
3. What is the total duration of the project according to your diagram?
4. Which activities lie on the critical path based on your calculation?
5. How would you adjust the LS and LF times if an activity's duration changes?

**Tip:** Double-check your connections between activities to make sure ES and EF align properly, especially on the critical path, where any mistake can cause project delays.

Explore how to calculate Early Start (ES), Late Start (LS), and Float (Slack) times using the Critical Path Method (CPM). This detailed guide covers step-by-step calculations and analysis to determine project timelines effectively.

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