Step 1: Phage typing of Staphylococcus aureus is used in epidemiology to fingerprint strains by checking which bacteriophages can lyse them, allowing outbreak strains to be traced.
Step 2: In the pattern method a fixed panel of 23 standard typing phages is spotted on the isolate. The unique combination of phages that produce lysis defines the strain.
Step 3: Naming follows the lysing phages; a strain lysed by 83A, 84 and 85 becomes type 83A/84/85. This pattern-based identity is the heart of the method.
Step 4: Because the recognised basic set holds 23 phages, the values 12, 15 and 20 are incorrect.
\[\boxed{23}\]