Find the smallest whole number of diners that makes every per-person share a whole number of cents.

What that answer leaves out

Compatibility does not identify the actual event.

Excluded world. Another divisor shared by all printed totals is left out.

Keep the arithmetic condition attached to the candidate.

Excluded world. A candidate that leaves a fractional-cent share is excluded.

Trying a count does not satisfy divisibility.

Excluded world. A candidate leaving a remainder is included despite being excluded by the cents rule.

Divisibility contains no performance observation.

Excluded world. A dinner with the same totals and different service is left out.

candidate denominators up to a stated ceiling — enumerable. No mesh state machine is claimed.

Write the nearest claim this example does not support.

Your words stay on this page. Nothing is sent or stored.

Teaches the recovery trick honestly, but the reachable space is not the feasible space of denominators. Does not clear N2. Do not argue it up.
These are self-audited digital models, not independently verified physical devices.
No learner efficacy, transfer, accessibility equivalence, or vendor performance has been measured.
Unbounded and temporal devices remain text exercises; no faithful state machine is asserted for them.
The receipt exercise has no supplied totals or ceiling, so it supports no computed denominator here.

Look away from the object, then answer the question again. This is a prompt for reflection, not a measured learning outcome.

What does a compatible denominator establish?