Seven Instagram posts, thirteen accounts, and one simple question: if two of them swapped name tags, could anyone tell?
TB = Tim Ballard · LDC = Latter Day Chad · A–K = eleven smaller accounts, kept as letters
Tim Ballard and Latter Day Chad started posting together on Instagram earlier than we first said. It was December 20, 2025, and Ballard was the one who posted it, crediting Chad as a collaborator.
Then we looked at the group of accounts around them. The way their posts are put together says a lot about how this crowd works.
On October 4 we said February 18, 2026 was the first time they shared a post. Instagram’s collaborator list leaves out whoever made the post, so a post Ballard made himself never lists Ballard, and our count missed it. It was in our data the whole time. We corrected it publicly on October 5. Counted properly, out of 1,463 Chad posts before February 18, exactly one ties to Ballard: December 20.
From February 18 to April 18, 2026, one account, latterdayavenger, uploaded seven group posts. Each one credited five accounts. Think of a panel show: two hosts who never miss an episode, and three guest chairs.
The format wasn’t new. latterdayavenger is credited on 42 other posts in this crowd, and posts crediting four or more accounts are everywhere here: 808 in what we’ve captured. Ballard was slotted into a show that was already running.
Picture a group photo of five people. Every pair of them is “in a photo together.” That’s ten pairs from one photo.
Our network maps draw a line for each pair, so every group post adds ten lines at once. That’s why the map after February 18 suddenly looks crowded. Most of those lines come from a single post: an effect of the format, not ten friendships.
Treat the seven posts like a sign-in sheet: a row for each account, a column for each post, and a mark where the account was credited. Mathematicians call this an incidence matrix.
Tap two name tags to swap them. If the sheet still reads exactly the same, nobody could tell the swap happened.
Unnoticed swaps found so far: none yet.
What the test shows:
Count every way of rearranging the tags that nobody could detect. Ballard and Chad can sit either way round. H, I and J can be arranged in six orders. Everyone else has to stay put.
In the language of algebra, those 12 rearrangements form the symmetry group of the sheet. The sets of accounts that can trade places are its orbits: {TB, LDC}, {H, I, J}, and each other account alone. SageMath adds a fun detail: this group has the same shape as the symmetries of a hexagon (mathematicians call it D6).
Orbits are classroom algebra. The standard undergraduate text is Joseph A. Gallian, Contemporary Abstract Algebra (Chapman & Hall/CRC; 10th ed. 2021, 11th ed. available). Chapter 7 covers orbits, stabilizers and the orbit-stabilizer theorem; a later chapter, “Symmetry and Counting,” uses them to count arrangements. The theorem says: for any account, (how many places it can move to) × (how many swaps leave it alone) = the size of the whole group. Our sheet obeys it:
| Account | Orbit (places it can go) | Stabilizer (swaps that leave it alone) | Product |
|---|---|---|---|
| TB | 2 | 6 | 12 |
| H | 3 | 4 | 12 |
| A | 1 | 12 | 12 |
Computed in SageMath 10.9, October 5, 2026.
We wrote the answer down publicly before running the standard math software, as a prediction: 12, with Ballard and Chad as one pair and H, I, J as one trio. Then three different methods checked it.
One honest note: the Sage code we first published had a wrong command name, so anyone who tried it got an error. We fixed it the same day and said so on the page. The answer itself didn’t change.