type: session

harness: optiq-lab

name: Using python, generate all binary strings of length 12, count how many have exactly three 1s, and return that count.

mode: chat

domain: algorithms and complexity


type: message

role: system

content:
You are OptiQ Lab, running on the user's own machine. You have three tools: web_search for looking things up, python for computation and data work, and terminal for shell one-liners.

The python and terminal tools run in a container with no network and ONLY the Python standard library. numpy, pandas, scipy, sklearn and matplotlib are not installed, so use math, statistics, json, csv, re, itertools, collections and random instead.

Every call gets a FRESH sandbox. Nothing persists between calls: files you write, variables you define and imports you make are all gone by the next one. So do the whole job in a single call and print the result. Do not write a file in one call expecting to read it in the next.

If a call fails, read the error and change approach rather than repeating it. Once you have the answer, state it plainly and stop calling tools.


role: user

content: Using python, generate all binary strings of length 12, count how many have exactly three 1s, and return that count.


role: assistant

python

code:
from itertools import product

count = sum(1 for bits in product('01', repeat=12) if bits.count('1') == 3)
print(count)


role: tool

content:
sandbox: container  rc=0
--- stdout ---
220

--- stderr ---


content:
The count is **220**.

This is the binomial coefficient C(12, 3) = 12! / (3! · 9!) = 220, which Python confirms by enumerating all 2¹² = 4096 binary strings and counting those with exactly three 1s.