Daily Math Puzzle: 2026-09-16

Only Carol and Bob — Let's track the state of each module (Committed (Y) or Not Committed (N)) through the attempts: Initial State: Alice (N), Bob (N), Carol (N), David (N) 1. **David attempts to commit:** * David's rule: Requires Alice's Module IS committed (A:Y). * Current state: Alice's Module is Not Committed (A:N). Condition not met. * Result: David's commit fails. * State after David's attempt: A:N, B:N, C:N, D:N 2. **Carol attempts to commit:** * Carol's rule: Requires David's Module IS NOT committed (D:N). * Current state: David's Module is Not Committed (D:N) (his previous attempt failed). Condition met. * Result: Carol's commit succeeds. * State after Carol's attempt: A:N, B:N, C:Y, D:N 3. **Bob attempts to commit:** * Bob's rule: Requires Carol's Module IS committed (C:Y). * Current state: Carol's Module IS Committed (C:Y). Condition met. * Result: Bob's commit succeeds. * State after Bob's attempt: A:N, B:Y, C:Y, D:N 4. **Alice attempts to commit:** * Alice's rule: Requires Bob's Module IS NOT committed (B:N). * Current state: Bob's Module IS Committed (B:Y). Condition not met. * Result: Alice's commit fails. * State after Alice's attempt: A:N, B:Y, C:Y, D:N Therefore, only Carol and Bob successfully committed their modules.