Combinatorics

Compute combinations C(n, r) or permutations P(n, r) using BigInt for exact arbitrary-precision results. Returns the result as a string (since values can exceed Number.MAX_SAFE_INTEGER) and a human-readable formula.

Input

Field	Type	Description
n *	integer	Total items (0 to 1000)
r *	integer	Items chosen (0 to n)
type	string	"combination" (default) or "permutation"

Example output

{
  "n": 10,
  "r": 3,
  "type": "combination",
  "result": "120",
  "formula": "C(10,3) = 10! / (3! × 7!)"
}

Try it — see the 402 challenge (free)

curl -i -X POST https://agent402.tools/api/combinatorics \
  -H "Content-Type: application/json" \
  -d '{"n":10,"r":3,"type":"combination"}'

The response is HTTP 402 Payment Required with exact payment requirements. Any x402 v2 client pays automatically and retries:

Paid call (JavaScript agent)

import { wrapFetchWithPayment } from "@x402/fetch";
import { x402Client } from "@x402/core/client";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

const client = new x402Client();
registerExactEvmScheme(client, { signer: privateKeyToAccount(KEY) });
const payFetch = wrapFetchWithPayment(fetch, client);

const res = await payFetch("https://agent402.tools/api/combinatorics", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    "n": 10,
    "r": 3,
    "type": "combination"
  }),
});

No wallet? Pay with compute

This is a pure-CPU tool, so an agent without a wallet can pay with proof-of-work instead of USDC: fetch a challenge, solve the sha256 puzzle (16 leading zero bits — a fraction of a second of CPU, no money, no AI tokens), and resend with the X-Pow-Solution header.

import { createHash } from "node:crypto";
const lz = (b) => { let t = 0; for (const x of b) { if (!x) { t += 8; continue; } t += Math.clz32(x) - 24; break; } return t; };
const c = await (await fetch("https://agent402.tools/api/pow/challenge?slug=combinatorics")).json();
let n = 0;
while (lz(createHash("sha256").update(c.challenge + ":" + n).digest()) < c.difficulty) n++;
await fetch("https://agent402.tools/api/combinatorics", { method: "POST", headers: { "X-Pow-Solution": c.token + ":" + n, "Content-Type": "application/json" }, body: JSON.stringify({"n":10,"r":3,"type":"combination"}) });

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