# @stem_antics on Instagram

- **Type:** Video
- **Original URL:** https://www.instagram.com/p/DaaclOVA5A6
- **Gondola URL:** https://gondola.cc/posts/67635473-stem-antics-instagram
- **Thumbnail:** https://img.gondola.cc/tr:w-,h-,fo-auto/postThumbnails/c5183b7b72.jpg
- **Posted:** 2026-07-05T13:41:52.000+00:00
- **Account Owner:** Stem Antics (@stem_antics) — https://gondola.cc/stem_antics

## Caption

One poisoned bottle hides among a thousand. You have ten tasters and a poison that acts within the hour. Brute force means a thousand sips. Information theory does it in a single round, by turning each person into a bit.

Number every bottle from 0 to 999 in binary. A thousand labels fit inside ten binary digits, because 2^10 = 1024. Assign each taster to one bit position, from bit 0 up to bit 9.

The rule is purely mechanical:

- Taster i sips from every bottle whose binary label carries a 1 in position i
- Each person ends up drinking a cocktail drawn from hundreds of bottles at once
- Wait for the poison to act, then read off who falls ill

Take bottle 742. In binary that is 1011100110. Tasters 1, 2, 5, 6, 7 and 9 all sip from it, so if 742 is the guilty one, exactly those six collapse and the remaining four stay standing.

The pattern of sick and healthy tasters is a ten-bit word. A collapsed taster marks a 1, a survivor marks a 0. Line them from bit 9 down to bit 0 and you have read the binary address of the poisoned bottle straight off their bodies. Convert to decimal and you are standing in front of it.

This is Shannon made physical. Pinning one option out of N demands log2(N) bits of information. log2(1000) is roughly 9.97, so ten independent yes-or-no channels are not merely sufficient, they are the theoretical floor. Nine tasters could only ever separate 512 bottles, less than a thousand. The tenth is what carries you over the line, and no clever scheme can do it with fewer.

No single taster knows the answer. It lives entirely in the correlation between them.

Measurement is just the art of asking the fewest questions that still corner the truth.

#stemantics #informationtheory #binary #shannon #stemeducation

## Stats

- **Views:** 6,254
- **Likes:** 244
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- **Comments:** 10

## Tags

informationtheory, stemeducation, binary, shannon, stemantics

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