Example · Everyday puzzle

Rhythmic knocking upstairs

"Fixed window plus even interval" is the key: it narrows the field from "someone deliberately knocking" to something period-driven, such as a device or a pipe.

现象 · QUESTION

There is a dull, rhythmic knocking from upstairs every night between about 23:00 and 01:00 — what is it most likely to be?

已知线索 · CLUES5 条

Timing: roughly 23:00–01:00, most nights
Interval: about every 30 seconds, fairly even
Duration: for the last ten days, one to two hours per night
Character: a low "thud", not a sharp knock
Context: almost never audible during the day; the upstairs neighbour keeps late hours

可能性排序 · HYPOTHESES概率为估计，不是结论

1. A timed appliance (washer / dryer / dishwasher)about 45%

依据：Fixed window and even interval fit a program cycle; a low thud is consistent with vibration transmitted through the floor slab

2. Pipe expansion or a circulation pumpabout 25%

依据：Heating or hot-water pipes tick as they expand and cool, usually when heating stops — but less evenly spaced than this

3. Floorboards or furniture settling with temperature changeabout 15%

依据：Wood moves as temperature and humidity shift, typically around a temperature turning point

4. Human activity (walking, tidying, moving things)about 10%

依据：Possible, but "once every 30 seconds for two hours" does not match natural activity

5. Something else (a pet, leftover work, deliberate knocking)about 5%

依据：Needs extra assumptions; ranked last by Occam's razor

怎么验证 · VERIFY

Log start time, end time and each interval for three nights, noting whether weekends differ
Note whether water, motor or footstep sounds accompany it
Listen at the wall corner and the pipe shaft while it happens to judge direction
Ask (casually, by day) whether new appliances arrived recently, and check your own hot-water use

场景还原 · RECONSTRUCT

If it is a night-time wash/dry cycle, the sound should change in stages — fill, tumble, spin — and stop entirely after an hour or two. If it is pipe expansion, the noise clusters around when water is heated or stops being heated, and lines up with building-wide water use. The two differ clearly in whether the sound evolves in stages.

复盘 · REVIEW

The value here is not guessing correctly but using "fixed window + even interval" to narrow to something periodic, then spending a few nights distinguishing a device from a pipe. It costs nothing, needs no confrontation, and can be settled within a week.

本页是一次推演示例：结论为概率性推断，不是事实认定，也不构成任何专业建议。你的线索与结果不会被保存。想自己推一次，见推演台；方法见方法论。