Collection-day planning: 祝日 cancellation, 第n週 rules, and a booking deadline
川口さん lives alone in a 市 whose rules are printed on a fridge magnet: 可燃ごみ is collected on 火・金; 資源ごみ（びん・缶・ペットボトル）on the 第2・第4水曜; collection is cancelled on 祝日 with no 振替; everything must be out by 8:00 on the day; 粗大ごみ needs a phone booking at least one week before the 第4木曜 collection day. Today is Sunday 4月20日 (2025). She leaves on Monday 4月28日 and returns late on Thursday 5月1日. She has one full bag of 可燃ごみ, a box of ペットボトル, and a 学習机 she wants gone before she travels. In 2025, 4月29日 is 昭和の日, a Tuesday.
1. On which date, and by what time, must 川口さん put out the 可燃ごみ so that it is actually collected before she leaves? Show the dates you considered and rejected.
Read the worked answer
- 可燃 = 火・金. In the window 4/20–4/27: 火 4/22 and 金 4/25 are collection days. Monday 4/28, her departure day, is neither - she cannot put it out "on the way out".
- 4/29 (火) is 昭和の日 → no collection, and the magnet says no 振替. Because she is also away, that date is doubly unusable.
- So the last usable date is 4/25 (金), out by 8:00. 4/22 is earlier and equally valid if the bag is already full.
- The judgement point: the holiday rule makes 4/25 more valuable than it looks. If she skips it, the next 可燃 is 5/2 (金), which means roughly a week of smelly rubbish in the flat after she returns - so 4/25 is not "one of two options", it is the deadline.
2. When can the ペットボトル be collected, and what happens if she is too busy to deal with them before the trip?
Read the worked answer
- 資源 = 第2・第4水曜. April 2025 Wednesdays are 2, 9, 16, 23, 30 → 第2 = 4/9 (past), 第4 = 4/23.
- 4/30 is the 5th Wednesday and is not a 第2 or 第4 Wednesday, so it is not a collection day even though it is the last Wednesday of the month. Counting "week of the month" rather than "how many Wednesdays" is exactly the trap.
- She is at home on 4/23, so: out by 8:00 on 4/23. That is before her trip, so no conflict.
- If she misses it: the next 資源 day is 5/14 (第2水) - about three weeks of storing bottles. That is why 4/23, though not urgent-looking, is the practical deadline.
3. She wants the 学習机 collected before she leaves. Can she arrange it? Show the arithmetic and say what she must not do on 4/24.
Read the worked answer
- 粗大ごみ = 第4木曜. April 2025 Thursdays are 3, 10, 17, 24 → the collection day is 4/24.
- Booking must be made at least one week before that date → the call had to be made by 4/17. Today is 4/20, so that window has already closed. She cannot get the desk collected on 4/24 no matter what she does now.
- Next opportunity: 第4木曜 of May = 5/22, bookable from 5/1 (at least a week before). This is after her return, so the realistic plan is: leave the desk, book when she is back.
- Absolute prohibition: putting the desk out on 4/24 without a booking. Unbooked 粗大ごみ is 不法投棄, is not collected, and can be traced back to her. "There is a collection day that day" does not mean "anything may be put out that day".