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# The Man Who Counted

[GitHub](https://github.com/HectorTablero/QED-Scripts/blob/main/Magazine%204/The%20Man%20Who%20Counted/pearlBalance.js) (Open Source, MIT License) | [Live Demo](https://qed.mat.uam.es/revista/articulo/el-hombre-que-calculaba)

**Date:** July 2026
**Technologies:** JavaScript, Tailwind CSS

---

## Overview

PearlBalance makes playable the classic logic puzzle the review's protagonist Beremiz solves: among eight identical-looking pearls, one is slightly lighter, and it must be identified with certainty using a balance scale in only two weighings. The book states the puzzle and moves on without ever printing the solution, so this element supplies the balance itself.

Each weighing has exactly 3 outcomes (left pan down, right pan down, balanced), so $n$ weighings distinguish at most $3^n$ possible states. To pin down 1 light pearl among $N$ candidates requires $3^n \ge N$; with $N=8$ pearls, $3^1=3 < 8$ but $3^2=9\ge8$, so two weighings is the information-theoretic minimum, and the puzzle's constraint is exactly tight — every one of the $3^2=9$ possible weighing-outcome pairs must be used to distinguish an outcome, with only one spare.

## Implementation Details

### Setup and Interaction

The light pearl is randomized on every reset rather than fixed, so the puzzle cannot be solved once and remembered. Clicking a pearl cycles it through three positions — aside, left pan, right pan:

```javascript
::: js PearlBalance
8, 2
perlas1
autoPlay, allowFullscreen, openControls, h=100
:::
```

### Weighing Logic

A "weigh" action only proceeds if both pans hold an equal, non-zero number of pearls, and refuses once the weighing budget (2, matching the book's constraint) is exhausted. The result — balanced, left pan rises, or right pan rises — is reported both as a beam tilt animation and as a text readout naming which side is lighter.

### Accusation

Once weighings run out, an "accuse" mode lets the reader tap the pearl they believe is the light one; the accused pearl is highlighted green or red depending on whether the guess was correct.

### Technical Considerations

The layout function computes pearl positions for the "aside" row and both pans dynamically from the current pearl counts in each group, so the pan contents rearrange themselves cleanly as pearls are dragged between positions rather than requiring fixed slots.