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# Brute Force - a product rule for counting puzzle
- URL: https://www.esheets.io/product-rule-for-counting-puzzle/
- Published: 2026-05-08T18:09:14.000Z
- Updated: 2026-05-08T19:32:01.000Z
- Author: Richard Linnington
- Tags: Maths, Puzzles

You have been hired as a junior security analyst. Your job is to calculate how many possible codes or arrangements a brute-force attacker would need to check.

For each mission, ask yourself three questions: how many choices are there at each stage, are repeats allowed, and does the order matter? Multiply the choices carefully — and watch out for situations where repeated or duplicate arrangements should not be counted.

# Brute Force: Security Analyst

🔊 Sound ON Toggle Mute 

## System Initialised

Welcome, trainee. You have been recruited as a Junior Security Analyst.

Your objective: evaluate the structural integrity of various security systems by calculating how many possible codes, arrangements, or groups a brute-force attacker would need to check.

We need precise calculations. Familiarise yourself with the basic protocols.

Begin Mission 

## Mission 1.0

## Level 1 / 10

**STANDARD ANALYST PROTOCOL - Ask yourself:** 
- How many choices are there for each stage?
- Are repeats allowed?
- Does the order matter?

Loading scenario... 

Submit Analysis Request Hint Reveal Working Scaffold 

Proceed to Next System 

## Mission Complete

Master Security Analyst

Systems Cleared

10/10

Final Score

1000

Solved 1st Try (No Help)

0

Wrong Attempts

0

Worded Hints Used

0

Scaffolds Revealed

0

Request New Mission