Combinatorics

{
  "asOf": "2026-10-11T06:26:05.813Z",
  "catalan": "29869166945772625950142417512",
  "combinations": "2598960",
  "combinationsWithRepetition": "3819816",
  "degraded": false,
  "derangements": "29672484407795138298279444403649511427278111361911893663894333196201",
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "factorial": "80658175170943878571660636856403766975289505440883277824000000000000",
  "factorialDigits": 68,
  "factorialScientific": "8.06581e+67",
  "k": "5",
  "n": "52",
  "notChecked": [
    "problems that need the inclusion-exclusion or Stirling-number setups beyond these standard counts",
    "results are exact; very large values are also given in scientific notation (approximate)"
  ],
  "permutations": "311875200",
  "permutationsWithRepetition": "380204032",
  "reasons": [
    "Exact big-integer arithmetic. Derangements: permutations with no fixed point. Catalan(n) = C(2n,n)/(n+1).",
    "Order matters for permutations, not for combinations."
  ],
  "source": "computed locally",
  "summary": "C(52,5) = 2598960; P(52,5) = 311875200.",
  "verdict": "COUNTED"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://math-stats.x402tookit.com/combinatorics?k=5&n=52'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://math-stats.x402tookit.com/combinatorics?k=5&n=52' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

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

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fmath-stats.x402tookit.com%2Fcombinatorics
const res = await pay("https://math-stats.x402tookit.com/combinatorics?k=5&n=52");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://math-stats.x402tookit.com/combinatorics?k=5&n=52")
    print(res.status_code, res.text)