Five pieces of thinking we found worth chewing on. If your answer feels obvious, look again.
1. The Two-Test Paradox
A medical test for a rare disease (prevalence 1 in 10,000) has 99% sensitivity and 99% specificity. You test positive. The doctor sends you to a specialist, who runs the same test independently. Also positive.
What is the probability you actually have the disease?
About 49.5% — still a coin flip.
The first positive moves your probability from 1/10,000 to roughly 1%, not 99%. Why: among 10,000 people, about 1 truly has the disease (and tests positive ~99% of the time = 0.99 true positives), while ~9,999 don't (and 1% test positive anyway = ~100 false positives). One real signal drowning in a hundred false ones.
The second independent positive uses 1% as the new prior, giving roughly 50/50. Two highly accurate tests on a rare condition leave you genuinely uncertain.
The lesson isn't about medicine. Base rates dominate intuition in any low-prevalence detection problem: spam filters, fraud alerts, terrorist screening, AI-generated content classifiers. Confidence in the test is often misplaced confidence in the world.
2. The Drilled Cube
You have a 3×3×3 cube assembled from 27 unit cubes. You drill a straight hole through the exact center along each of the three orthogonal axes (x, y, z) — three drills total, each one passing through three unit cubes.
How many unit cubes are completely untouched?
20 untouched cubes.
Each drill removes 3 cubes. Three drills × 3 cubes = 9, but the drills overlap. By inclusion-exclusion: each pair of drills shares only the dead-center cube (one shared cube per pair, three pairs), and all three drills share that same center cube.
The puzzle rewards stopping before the obvious arithmetic. Subtract 9, get 18, feel done — and you're wrong.
3. AI or Not
Below are four short passages. For each, decide whether it was written by an AI or by a human. Go with first instinct.
Passage A
In today's rapidly evolving digital landscape, the relationship between technology and human creativity continues to transform in fascinating ways. Whether through enhanced collaboration tools, AI-assisted workflows, or novel forms of artistic expression, we are witnessing changes that touch every aspect of how we create. As we navigate this exciting frontier, it remains essential to think carefully about both the opportunities and the challenges ahead.
Passage B
My grandfather kept a workshop in the garage with exactly four tools hanging from a pegboard, in the same order, for forty-one years. When he died we found a fifth nail. He had drawn an outline of a wrench around it in pencil, but never bought the wrench. I think about that nail more than I should.
Passage C
The trouble with productivity advice is that almost all of it was written by people who were already productive when they sat down to write it. Survivor bias, basically. The advice that would actually help — what the unproductive person tried, why it failed, what they did instead — never gets written, because the person is, by definition, not writing it.
Passage D
There's something deeply satisfying about a well-organized spreadsheet — the alignment of columns, the consistency of formatting, the way data finally tells its story when properly arranged. It's a small form of beauty, often overlooked. Yet in our rush toward more sophisticated tools, we sometimes forget that the humble grid still has much to teach us about clarity of thought.
All four were written by an AI — the same one that wrote this page.
The exercise wasn't "spot the AI." It was "notice that you can't reliably spot the AI when it's trying." Passage A leans on tells most readers associate with AI: hedging, balance, "navigate this frontier," vague abstraction. Passage B uses tells most readers associate with humans: specific numbers, concrete objects, restrained sentiment, slight asymmetry. Passages C and D sit somewhere in between. One model produced all four, on demand.
If you scored 4/4 you used aesthetic priors that happened to align with the writer's intent in each passage. Those priors are losing predictive power every month.
The MainBrains question isn't whether AI can fool you in 2026. It's what an internet built on this assumption ought to look like.
4. The Honest Liar
You meet two people, A and B. Each is either always-truthful or always-lying.
A says: "Exactly one of us is lying." B says: "A is telling the truth."
Who is lying?
Both are lying.
Suppose A is truthful. Then exactly one of them is lying — and since A is truthful, B must be the liar. But B says "A is telling the truth," which would then be a true statement from a liar. Contradiction.
So A must be lying. A's statement "exactly one of us is lying" is false, meaning either zero or two of them are lying. Since A is lying, the count is two. B's statement is also false (A is not telling the truth). Fully consistent.
The trick is resisting the assumption that B's endorsement of A carries information. A liar's endorsement is just another lie.
5. The Light Bulb Marathon
One hundred light bulbs sit in a row, all switched off. You make 100 passes down the line. On pass n, you toggle (flip the state of) every nth bulb. So pass 1 toggles every bulb; pass 2 toggles every second; pass 3 every third; and so on, ending with pass 100 which toggles only bulb 100.
After all 100 passes, which bulbs are on?
The perfect squares: bulbs 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
A bulb gets toggled once for each of its divisors. Bulb 12 has divisors 1, 2, 3, 4, 6, 12 — six toggles, ends off. Divisors normally come in pairs (d and n/d), so the count is even and the bulb returns to its starting state.
The exception: perfect squares. For 16, the divisor 4 pairs with itself (4 × 4 = 16), so it counts only once, breaking the pairing. Square numbers have an odd divisor count and end up on.
The puzzle is loved because the answer reveals a deep fact about numbers — the parity of the divisor function — through a problem that sounds like janitorial work.
More to come. If you have a teaser worth adding, write us.