The Barangay Clearance Queue
A barangay hall processes clearance requests at one window. Each morning the clerk opens at 8:00 AM with a stack of 48 pending applications already on the desk, filed in the exact order received. The clerk must follow three rules: (1) applications are served strictly first-come, first-served by the number written on the folder; (2) any folder missing a cedula copy is set aside into a 'hold' pile and reinserted at the bottom of the main stack only after the rest of the original stack is served; (3) no more than 15 folders may be served before a 10-minute break. On this morning, folders numbered 7, 19, and 33 are missing cedula copies. Folder 19 is the only one belonging to a senior citizen who has been waiting since 7:15 AM. The clerk's supervisor asks whether the senior citizen can be served before noon without breaking any rule.
1. Trace the order in which folders 7, 19, and 33 are served, and state whether folder 19 reaches the window before folder 33.
Read the worked answer
Folders 7, 19, 33 are pulled from the main stack when reached and placed on hold. The main stack continues 1-48 in order, skipping those three. After folder 48 is served, the hold pile is reinserted at the bottom in the order it was set aside: 7 first, then 19, then 33.
So the service order is: 1-6, 8-18, 20-32, 34-48, then 7, 19, 33.
Folder 19 is served before folder 33 (19 comes second in the hold pile). Rule (2) says reinsertion happens only after the rest of the original stack is served, so the senior citizen's folder cannot jump the queue - seniority is not an exception listed in the rules.
2. Given the 15-folder break rule, identify the folder number being served when the second break begins, and explain whether the senior citizen is served before or after that second break.
Read the worked answer
Count served folders: break after #15, #30, #45.
- Break 1 after the 15th folder served. Serving order 1-6, 8-18: the 15th served is folder 16 (1-6 = 6 folders, 8-16 = 9 more, total 15).
- Break 2 after the 30th folder served. Continuing 17, 18, 20-32: folders 17 and 18 bring the count to 17; then 20-32 adds 13 more → count 30 at folder 32.
- Break 3 after the 45th served: 34-48 adds 15 → the 45th served is folder 48.
The senior citizen's folder 19 is served in the hold pile, which begins only after 48. That is after the third break, not the second. The senior is served after all three breaks.
3. The supervisor proposes serving folder 19 immediately when it is pulled, calling it a 'special case.' Using only the stated rules, evaluate this proposal and state the minimum rule change required to make it valid.
Read the worked answer
Serving folder 19 immediately violates rule (1) first-come-first-served and rule (2), which fixes the reinsertion point at the bottom after the original stack. 'Special case' is not among the listed rules, so the proposal is invalid as written.
The minimum change is to amend rule (2) to add a priority exception: folders flagged for senior citizens, persons with disability, or pregnant applicants are reinserted at the top of the main stack rather than the bottom. That single amendment makes immediate service of folder 19 consistent with the rules. Simply ignoring the rule is not a fix because it leaves the process undefined for future cases.