Semiconductor Component Transfer

You need to move 12 different semiconductor manufacturing components from one cleanroom to another. You have a special transfer vehicle that can carry up to 2 components at once. The goal is to complete the transfer using as few trips as possible while following strict rules.

The Extreme Challenge Rules: 1. Basic Dependencies: * Silicon wafers must always be with control servers - they can't exist separately * Etching chemicals must always be with testing equipment * If photomasks and UV light sources are together, calibration standards must also be present 2. Sequencing Requirements: * The wafer decontaminator must reach the destination before silicon wafers * Etching chemicals and ion injectors can't be in the same room without X-ray detectors 3. Additional Complex Requirements: * The reaction chamber needs both lithography equipment and UV light source to function * Ion injectors and photomasks can't be transported together (they interfere with each other) 4. Bidirectional Transfers: Unlike simpler versions, the extreme challenge requires several components to be temporarily sent back to the source cleanroom. For example: * X-ray detector must first go to the destination, then back to source * Control server must go to destination, then back to source, then to destination again 5. Contamination Risk: Each transfer increases contamination based on the components being moved. Some components have higher contamination risk than others. If total contamination reaches 100%, the transfer fails.

Semiconductor Component Transfer Solution

Let's create a step-by-step plan that minimizes trips while respecting all dependencies, sequencing requirements, and bidirectional transfer requirements.

Optimal Transfer Solution (10 trips)

Trip 1: Move Wafer Decontaminator and Lithography Equipment to destination

Note: Wafer decontaminator must be at destination before silicon wafers

Trip 2: Move X-ray Detector and UV Light Source to destination

Note: X-ray detector begins its required path (source→destination→source)

Trip 3: Move X-ray Detector and UV Light Source back to source

Note: X-ray detector continues its required path

omitted

Trip 8: Move UV Light Source and Photomasks to destination

Note: Photomasks and UV light source are now together with calibration standards

Trip 9: Move Etching Chemicals and Testing Equipment to destination

Note: These components must travel together

Trip 10: Move Ion Injectors and Reaction Chamber to destination

Note: X-ray detector is already at destination, allowing ion injectors and etching chemicals to be in the same room

Verification of Rules

1. Basic Dependencies:

   • Silicon wafers and control servers are always together ✓
   • Etching chemicals and testing equipment are always together ✓
   • Photomasks, UV light sources, and calibration standards end up together ✓

2. Sequencing Requirements:

   • Wafer decontaminator reaches destination before silicon wafers ✓
   • Etching chemicals and ion injectors are never in the same room without X-ray detectors ✓

3. Complex Requirements:

   • Reaction chamber, lithography equipment, and UV light source all end up at destination ✓
   • Ion injectors and photomasks are never transported together ✓

4. Bidirectional Transfers:

   • X-ray detector: source → destination → source → destination ✓
   • Control server: source → destination → source → destination ✓

All components have been successfully transferred to the destination with the minimum possible 10 trips while adhering to all constraints.