RE: Geiger counters(答えつき)

There are 13 gold coins, one of which is a forgery containing radioactive material. The task is to identify this forgery using a series of measurements conducted by technicians with Geiger counters.

The problem is structured as follows:

1. Coins: There are 13 gold coins, numbered 1 through 13. Exactly one coin is a forgery.

2. Forgery Characteristics: The forged coin contains radioactive material, detectable by a Geiger counter.

3. Technicians: There are 13 technicians available to perform measurements.

4. Measurement Process: Each technician selects a subset of the 13 coins for measurement. The technician uses a Geiger counter to test the selected coins simultaneously. The Geiger counter reacts if and only if the forgery is among the selected coins. Only the technician operating the device knows the result of the measurement.

5. Measurement Constraints: Each technician performs exactly one measurement. A total of 13 measurements are conducted.

6. Reporting: After each measurement, the technician reports either "positive" (radioactivity detected) or "negative" (no radioactivity detected).

7. Reliability Issue: Up to two technicians may provide unreliable reports, either due to intentional deception or unintentional error.

8. Objective: Identify the forged coin with certainty, despite the possibility of up to two unreliable reports.

♦Challenge♦
The challenge is to design a measurement strategy and analysis algorithm that can definitively identify the forged coin, given these constraints and potential inaccuracies in the technicians' reports.