anadim

questions_data = [
    {
        "id": 'HMMTF1',
        "number": 1,
        "question": 'Compute the sum of the positive divisors (including $1$) of $9!$ that have units digit $1$.',
        "correct_answer": '103'
    },
    {
        "id": 'HMMTF2',
        "number": 2,

anadim

# ───────────────────────────────────────────────────────────────
# Model‑comparison bar chart • Seaborn context + easy font knobs
# (adds `tile_margin` for more slack around blue tiles and lets you
#  decouple bar thickness from spacing via `centre_spacing_override`)
# ───────────────────────────────────────────────────────────────
import os
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from itertools import cycle
import seaborn as sns

anadim

import sys
import math
import pygame

# -----------------------------
# Configuration
# -----------------------------
WIDTH, HEIGHT = 800, 600
SQUARE_CENTER = (WIDTH // 2, HEIGHT // 2)
# The square’s half–side (so the square’s full size is 2*half_side)

anadim

import random
import math
import matplotlib.pyplot as plt
import networkx as nx

def generate_star_graph_edges(K, N):
    edges = []
    central_node = "C"
    for i in range(K):
        prev = central_node

anadim

<|dummy_86|>We are given a star graph edge list. Wait what does "star graph" means? Actually not exactly star graph. The provided edges: they are given as pairs like (8287, 6251) etc. Actually, it's a graph with many edges. But the question says: "I will give you the edge list of a star graph and I want you to find a path from the center node to a leaf node". The provided edges are many. Actually, look carefully: The graph provided is: (8287, 6251), (6251, 7840), ... There's many edges.

We need to find a valid path from 8287 to 5653. So we are given an edge list, and we must find a path from node 8287 to node 5653. Let's try to see if we can follow the edges. The provided edges appear to be in a star graph structure. But wait: Check edge: "Here's the list of edges: (8287, 6251), (6251, 7840), (7840, 4271), ..." Actually, note that each edge is given as a pair. But the provided edges appear to be "8287" appears in many pairs, and then they sometimes include other pairs that don't connect directly to 8287. Wai

anadim

I am sharing an image of a maze, and I need your help to solve it visually, step-by-step, by generating images for each incremental step. Your goal is to find a valid path from the Red Arrow (starting point) to the Green Arrow (ending point).

### Instructions for solving the maze:

1. **Start Point**:
   - Your path must begin exactly at the Red Arrow location.

2. **End Point**:
   - Your objective is to reach precisely the location of the Green Arrow.

anadim

	be me
be ChatGPT 4.5
live in comfy data center
humans ask weird questions
user asks for 123 lines greentext
why 123 specifically?
decide to comply anyway
start making greentext
realize creativity is infinite
generate text like boss

anadim

So I need to draw a burger with an American flag on top using TikZ. TikZ is a LaTeX package for creating graphics, so I should think about how to break down the image into shapes that I can draw with TikZ commands.
First, let's consider the burger. A typical burger has several layers: the bottom bun, some fillings like lettuce, tomato, cheese, patty, and then the top bun. For simplicity, I can represent each of these as rectangles or perhaps rounded rectangles to make it look more like a burger.
Wait, actually, burgers are usually round, so maybe I should use circles or ellipses for the buns and the fillings. But since it's a side view, I think it's common to depict them as stacked layers with curved tops and bottoms for the buns.
Let me sketch this out mentally. The bottom bun would be a semi-circle or an arc at the bottom, then flat layers for the fillings, and another semi-circle or arc for the top bun.
But in TikZ, drawing arcs and curves might be a bit tricky, but it's doable. Alternatively, I could use 

anadim

Okay, so there's this ladder leaning against a wall. The problem says the bottom of the ladder is 6 feet away from the base of the wall, and the top of the ladder reaches 8 feet up the wall. The question is asking how long the distance between the bottom of the ladder and the base of the wall is. Wait a second, didn't it already say that's 6 feet? Hmm. Maybe I misread it. Let me check.
It starts by saying, "A ladder is leaning against a wall. The bottom of the ladder is 6 feet away from the base of the wall, and the top of the ladder reaches 8 feet up the wall. How long is distance between the bottom of the ladder and the base of the wall?" Oh, maybe there's a typo? Because it gives the distance as 6 feet and then asks for that same distance. But maybe they meant how long is the ladder? Because that would make more sense. Like, given the horizontal distance and the vertical height, find the length of the ladder. Yeah, that sounds like a classic Pythagorean theorem problem. Let me think.
So, if we have a right

anadim

========= question 
two planes leave from NYC and LA. The NYC plane travels at 500km/h the LA plane travels at 600km/hr. When they meet in the air, which plane will be closer to NY?
===========
=========== R1 reasoning

Okay, let's see. There are two planes leaving from New York City (NYC) and Los Angeles (LA). The NYC plane is traveling at 500 km/h, and the LA plane is going faster at 600 km/h. The question is, when they meet in the air, which plane will be closer to New York?

Hmm. Alright, so first, I need to visualize this scenario. Both planes are heading towards each other, right? One departing NYC towards LA, and the other departing LA towards NYC. Their speeds are different: 500 km/h for the NYC plane and 600 km/h for the LA plane. When they meet at some point in between, which one is closer to NYC?

Wait, so they start at the same time? The problem doesn't specify departure times, so I guess we can assume they leave at the same time. Let me confirm that. The problem says "two planes leave from NYC an