Rules
Part of Who actually publishes the state calendars that set a deadline?
Fifteen worked examples of business day counting across stacked closure layers
Fifteen worked examples over one invented three-layer closure arrangement in March 2027, counting and stepping business days with the arithmetic shown.
Every example below uses one invented arrangement of closure layers, applied to March 2027. None of it is any jurisdiction's real calendar, and no real closure date appears anywhere on this page.
The point is the behavior of layered lists, which is the same whatever the dates are. Substitute your own list and the pattern holds.
What to take away
- Adding a layer never moves a deadline earlier. It either moves it later or leaves it where it was.
- A layer that names two dates can remove one open day, because a date already closed by another layer costs nothing.
- Counting backward from a deadline and counting forward to one are different operations and do not have to meet in the middle.
The arrangement
Three layers, invented for this page. Saturday and Sunday are the rest days.
Three Layers and Their Dates
Layer A
- Dates named
- Wed 10 Mar
- New dates added
- 1
- Overlap with earlier
- none
Layer B
- Dates named
- Wed 10, 17 Mar
- New dates added
- 1
- Overlap with earlier
- 10 Mar
Layer C
- Dates named
- Mon 15, Tue 16 Mar
- New dates added
- 2
- Overlap with earlier
- none
| Layer | Dates it names |
|---|---|
| A | Wednesday 10 March 2027 |
| B | Wednesday 10 and Wednesday 17 March 2027 |
| C | Monday 15 and Tuesday 16 March 2027 |
Layer B repeats one of A's dates on purpose, because overlap is the normal case and the arithmetic has to handle it without special pleading.
Counting a span
1. The whole of March, rest days only: 23. Four whole weeks give 20 and the three leftover days, a Monday, Tuesday and Wednesday, give three more.
2. The whole of March with layer A: 22. One weekday closure, one day off the count.
3. The whole of March with A and B: 21. B names two dates but only the 17th is new, so the count drops by one rather than two.
4. The whole of March with A, B and C: 19. C adds two more weekdays, neither previously closed, so this time the count drops by two.
5. Monday 8 to Friday 12 March with layer A: 4. Five weekdays, one of them closed.
6. Monday 15 to Friday 19 March with layer C: 3. Five weekdays, two closed.
7. Monday 15 to Friday 19 March with B and C: 2. Three closures inside a five-weekday span.
8. Saturday 6 to Sunday 7 March with every layer: 0. No layer can reduce a count that was already zero. Whether a given day is open at all is a legal and commercial question before it is an arithmetic one, and the category itself is set out under business day.
9. The whole of 2027 with all three layers: 257. The year has 261 weekdays and the union of the three layers holds four distinct weekdays. The base figure is derived under counting a year.
Stepping to a deadline
10. Ten business days after Friday 5 March, no layers: Friday 19 March. Two full weeks of weekdays.
11. Ten business days after Friday 5 March with A: Monday 22 March. One closure inside the span pushes the answer past the weekend rather than by one calendar day.
12. Ten business days after Friday 5 March with A and B: Tuesday 23 March. The 17th falls inside the extended span, so it pushes again.
13. Ten business days after Friday 5 March with all three: Thursday 25 March. Two more closures, two more open days needed.
14. Five business days after Friday 5 March with A: Monday 15 March. Without A it would be Friday 12 March. One closure, one open day later, and again the weekend absorbs the shift.
15. Ten business days before Tuesday 31 March with A and B: Tuesday 16 March. Without the layers it is Wednesday 17 March. Counting backward, a closure moves the answer earlier, which is the opposite direction from the forward case and is the reason the two do not agree.
Examples 13 and 15 are worth putting side by side. Ten days forward from the 5th lands on the 25th, and ten days back from the 31st lands on the 16th. Neither is wrong. They are answers to different questions, and the mechanics of each are under adding business days and subtracting business days.
What each example does not settle
None of these answers is useful without knowing which layers apply to your obligation. A layer that binds courts may not bind banks, and applying a layer outside its scope produces a confident wrong answer with no symptom. Who publishes what, and what each publication governs, is under state and regional calendars.
The arithmetic itself is set algebra rather than subtraction, which is why example 3 drops by one and example 4 by two. Union is idempotent, so naming a date twice is free; summing the sizes of the lists instead would have given 20 for example 3 and no way to notice.
Common questions
Why do all the examples use one invented arrangement?
Because a real closure list belongs to a real body with a real publication date, and reproducing one here would strip both. The behavior being shown does not depend on the dates.
How were the answers produced?
Each was computed by walking the span day by day, and the counts were cross-checked against the weekday formula for the same span. The two methods fail differently.
Would a different set of invented dates change the pattern?
The numbers, yes. The pattern, no: overlap is free, a forward step and a backward step disagree, and closures near a weekend push further than closures midweek.
Can I use these figures for a real deadline?
No. Substitute the layers that actually apply to your obligation, with their publishers and retrieval dates, and recompute. The method transfers; these numbers do not.
