Assigning Four Roles with One Unreliable Statement
Four analysts - Moretti, Nakamura, Okafor and Pereira - are being assigned to the four roles on a product team: analyst, designer, engineer and tester. The staffing notes contain four statements. (1) Moretti will not be the analyst and will not be the tester. (2) Nakamura will take either the analyst or the designer role. (3) Okafor will be the engineer. (4) Pereira will not be the designer. The team lead treats all four statements as reliable and wants a single fixed assignment before the project kick-off. A colleague warns that statement (2) came from a conversation overheard in the cafeteria and may be wrong; the other three statements are documented. The lead must decide whether to publish the assignment now or wait for confirmation, knowing that changing roles after kick-off costs about two weeks of ramp-up for the team.
1. Assuming all four statements are true, determine each person's role.
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Work from the most restrictive statements:
- Statement (3) fixes Okafor = engineer.
- Statement (1) removes analyst and tester for Moretti. Engineer is taken, so the only remaining role is Moretti = designer.
- Statement (2) says Nakamura is analyst or designer; designer is now taken, so Nakamura = analyst.
- The only role left is tester, so Pereira = tester. This is consistent with statement (4), since tester is not designer.
Result: Moretti designer, Nakamura analyst, Okafor engineer, Pereira tester. The assignment is unique: at each step only one role remained possible.
2. If statement (2) is false, is a unique assignment still forced? Enumerate the possibilities.
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Statements (1), (3) and (4) still hold, so Okafor = engineer and Moretti = designer, exactly as before.
That leaves analyst and tester for Nakamura and Pereira. Statement (4) only rules out designer for Pereira, which is already irrelevant. So two assignments survive:
- Nakamura = analyst, Pereira = tester
- Nakamura = tester, Pereira = analyst
Both are consistent with every documented statement. Therefore the unique assignment depends entirely on statement (2); without it the lead cannot publish a single fixed assignment. The weak link is not the undocumented claim's plausibility but its load-bearing role: it is the only statement that separates the two remaining people.
3. What is the smallest additional reliable fact that would allow the lead to publish with certainty, and how should the cost of waiting affect the decision?
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Any single fact that separates Nakamura from Pereira on the analyst/tester pair restores uniqueness. Examples:
- 'Pereira is not the analyst' → Pereira = tester, Nakamura = analyst.
- 'Nakamura is not the tester' → Nakamura = analyst.
- A documented certification held by only one of them and required for the analyst role.
A fact that merely confirms statement (2) is stronger but not minimal, since it resolves both roles at once.
Decision: the Okafor and Moretti roles are documented and can be announced immediately. Only the analyst/tester split is at risk. If confirmation costs one phone call before kick-off, waiting dominates: the expected loss from a wrong assignment (two weeks of ramp-up, plus disruption) exceeds the cost of a short delay. If no confirmation is possible before kick-off, the lead should publish the two certain roles and flag the remaining split as provisional rather than assert a full assignment that may be wrong.