Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx agentmods add skills/sequenzia/agent-alchemy/math-and-combinatoricsnpx skills add sequenzia/agent-alchemy --skill math-and-combinatoricsgit clone --depth 1 https://github.com/sequenzia/agent-alchemyWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/sequenzia/agent-alchemy/math-and-combinatorics)<a href="https://agentmods.dev/skills/sequenzia/agent-alchemy/math-and-combinatorics"><img src="https://agentmods.dev/badge/skills/sequenzia/agent-alchemy/math-and-combinatorics.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5 | $0.00072 | $0.05043 |
| Opus 5 | $0.00036 | $0.02521 |
| Sonnet 5 | $0.00014 | $0.01009 |
| Haiku 4.5 | $0.00007 | $0.00504 |
Grade A, and why
math-and-combinatorics scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 5d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 493 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Math and Combinatorics Patterns
Mathematical and combinatorial problems appear frequently in competitive programming and algorithm design. They often hide behind constraints that look like brute-force problems but require algebraic shortcuts to meet time limits. This reference covers eight core pattern families with recognition signals, templates, and pitfalls.
Pattern Recognition Table
| Trigger Signals | Technique | Typical Complexity |
|---|---|---|
| "answer modulo 10^9+7", large product/sum | Modular Arithmetic | O(1) per operation |
| "count primes up to N", "smallest factor" | Sieve of Eratosthenes | O(N log log N) |
| "greatest common divisor", "least common multiple" | GCD / LCM | O(log min(a,b)) |
| "how many ways to choose", "combinations mod p" | Binomial Coefficients | O(N) precompute, O(1) query |
| "compute a^b mod m", "matrix recurrence" | Fast Exponentiation | O(log b) |
| "count arrangements", "distribute items into groups" | Counting Techniques | Varies |
| "count elements satisfying at least one", "derangements" | Inclusion-Exclusion | O(2^k) for k constraints |
| "two players, optimal play", "who wins" | Game Theory (Sprague-Grundy) | Varies by state space |
Constraint-to-Technique Mapping
- N up to 10^7 and asks about primes: Sieve of Eratosthenes.
- N up to 10^6 and asks "how many ways": Precomputed factorials + modular inverse for nCr.
- "modulo 10^9+7" anywhere in the problem: Modular arithmetic throughout; use modular inverse for division.
- Two players, finite game, no randomness: Sprague-Grundy theorem or direct DP on game states.
- "count subsets satisfying property" with small constraint count (k <= 20): Inclusion-exclusion over 2^k subsets.
- Linear recurrence with large N (10^18): Matrix exponentiation to compute nth term in O(k^3 log N).
- "distribute N items into K groups": Stars and bars, possibly combined with inclusion-exclusion for bounded constraints.
Individual Patterns
Modular Arithmetic
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 5d ago First seen · 493 lines · 72 tokens per session scan A 7537c73dc6ba
math-and-combinatorics is a skill published in the GitHub repository sequenzia/agent-alchemy (44 stars, last pushed 3mo ago), licensed MIT. It adds 72 tokens to every session and 5,043 once invoked, about $0.0004 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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