: How do I transition from a day to another smoothly in a short story that takes place over of seven straight days? I am working on a short story, narrated in third person, roughly 20 pages

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1. The answer you are looking for is transitions.
A transition is merely a way to indicate that a story element such as setting or time has changed. You can use these within a single sentence to combine two disparate ideas as a sentence to change the flow of a paragraph or as a paragraph or story itself. Star Wars V, The Empire Strikes back is an entire movie that is a transition.
In a short story, you shouldn't be transitioning more than a few times because you have to start up and stop your plot. A transition costs momentum and you have very little momentum in a short story.
Typically transitions are merely scene changes. You indicate them by adding an extra return, possibly punctuated with asterisks, a number, or page break as in a chapter break.
There are no correct answers, but you can read several stories to get an idea for how to do it. Since you need to be brief, it's probably best to make your transitions either simplistically short (page break/"On the next day...") or have them do real work by setting up the event in such a way that it defines a clear distinction in what's happening while also informing the reader as to what the new section is about.
Every transition consists of these elements:

End whatever you were talking about
Establish space between where you were and where you're going. (Literal space, punctuation, or phrasing.
Go somewhere new

The sun set. -break- The sun rose.
The dog left the kitchen, slid through the hall and out the doggy door.
Jim stood over the corpse, gun in his hand. -Chapter 2- Mary inspected her nails in the salon chair.
The bell rang and everyone left. The bell rang and everyone returned.
Luke Sky Walker looked out upon the plain and a double sunset as heroic music swelled. -screen wipe- Princess Leia huddles in a cold dark cell as stabby stabby horror music piddles around in the background.
Monday was the day it began to end.... Tuesday arrived like a bat out of hell... Wednesday ate the bat and ground its bones to dust... Thursday swept the dust away... Friday looked at the clean room and dumped glitter everywhere... Saturday it became clear, the glitter was never coming out... On Sunday they buried his disco-ball-like corpse.

2. Danger Will Robinson. You should be asking: Can this be a short story? And if it can, does the structure of a short story inform the type transition I can use?
There are two questions within your question; and unfortunately you're not doing all of the math correctly to be asking the totally correct question. Most short story writers who are coming from a novel background overcomplicate their stories. While what you intend to write could be a short story, it's actually already heading for novella lengths.
At minimum you're writing a 40 page story to do your elements justice. How do we get there?
2 formulas.

Pages = Words * Spacing (Single = 1; Double = 2) * 250
Words = ((Characters + Locations) * 750 ) * 1.5 * MiceQuotientElements

MiceQuotientElements

M : Milieu - Plot as Place : Entering/Leaving/Surviving
I : Idea - Plot as Knowledge : Understanding/Discovering/Disseminating
C : Character - Plot as Actor : Who Is This Person/What Are They Becoming
E : Event as Plot Point : Thing Has Happened->Deal with it

So, let's assume at least 2 characters. 1 location & 7 events

((2+1) * 750) x (1.5 * 7)
Simplified: 3 * 750 * 10.5 = 23,625 words.

Single spaced that's 40 pages. Or 80 at double spaced.
Which leads me to the recommendation of: Transition as minimilistically as possible. Potentially just with a section break like "day 1", "day 2", etc. Or, some clear event such as the ritual that starts a class and ends a class always happening at the beginning and opening of each section. Or, as recommended above "The next day... something something complete."
If you take a page to transition, that's 14 pages with only 6 pages for plot. Probably pretty boring and everything will suffer.

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