problem.html

<style>
* { box-sizing: border-box; margin: 0; padding: 0; }
.sheet { padding: 1.5rem 0; font-family: var(--font-sans); }
.brief { background: var(--color-background-secondary); border-radius: var(--border-radius-lg); padding: 1.25rem 1.5rem; margin-bottom: 1.5rem; border: 0.5px solid var(--color-border-tertiary); }
.brief h1 { font-size: 20px; font-weight: 500; color: var(--color-text-primary); margin-bottom: 4px; }
.brief p { font-size: 13px; color: var(--color-text-secondary); line-height: 1.6; }
.section { background: var(--color-background-primary); border: 0.5px solid var(--color-border-tertiary); border-radius: var(--border-radius-lg); padding: 1.25rem; margin-bottom: 1rem; }
.sec-header { display: flex; align-items: center; gap: 10px; margin-bottom: 14px; }
.sec-num { width: 30px; height: 30px; border-radius: 50%; display: flex; align-items: center; justify-content: center; font-size: 13px; font-weight: 500; flex-shrink: 0; }
.s1 { background: #EEEDFE; color: #3C3489; }
.s2 { background: #E1F5EE; color: #085041; }
.s3 { background: #FAEEDA; color: #633806; }
.s4 { background: #FAECE7; color: #712B13; }
.s5 { background: #E6F1FB; color: #0C447C; }
.sec-title { font-size: 15px; font-weight: 500; color: var(--color-text-primary); }
.sec-subtitle { font-size: 12px; color: var(--color-text-secondary); }
.given-box { background: var(--color-background-secondary); border-radius: var(--border-radius-md); padding: 12px 14px; margin-bottom: 14px; }
.given-label { font-size: 11px; font-weight: 500; color: var(--color-text-secondary); letter-spacing: 0.05em; text-transform: uppercase; margin-bottom: 8px; }
.given-grid { display: grid; grid-template-columns: repeat(auto-fit, minmax(160px, 1fr)); gap: 8px; }
.given-item { background: var(--color-background-primary); border: 0.5px solid var(--color-border-tertiary); border-radius: var(--border-radius-md); padding: 8px 10px; }
.given-item .val { font-size: 15px; font-weight: 500; color: var(--color-text-primary); font-family: var(--font-mono); }
.given-item .lbl { font-size: 11px; color: var(--color-text-secondary); margin-top: 2px; }
.task-list { list-style: none; }
.task-list li { display: flex; gap: 10px; padding: 9px 0; border-bottom: 0.5px solid var(--color-border-tertiary); font-size: 13px; color: var(--color-text-primary); line-height: 1.55; align-items: flex-start; }
.task-list li:last-child { border-bottom: none; }
.task-num { font-size: 11px; font-weight: 500; color: var(--color-text-secondary); min-width: 20px; padding-top: 1px; }
.formula { font-family: var(--font-mono); font-size: 12px; background: var(--color-background-secondary); padding: 2px 6px; border-radius: 4px; color: var(--color-text-primary); display: inline; }
.expected { display: flex; gap: 8px; flex-wrap: wrap; margin-top: 10px; padding-top: 10px; border-top: 0.5px solid var(--color-border-tertiary); }
.exp-label { font-size: 11px; font-weight: 500; color: var(--color-text-secondary); letter-spacing: 0.05em; text-transform: uppercase; width: 100%; }
.exp-pill { font-size: 12px; padding: 4px 10px; border-radius: var(--border-radius-md); border: 0.5px solid var(--color-border-tertiary); color: var(--color-text-secondary); font-family: var(--font-mono); }
.warn { background: #FAEEDA; border-radius: var(--border-radius-md); padding: 8px 12px; font-size: 12px; color: #633806; margin-top: 10px; line-height: 1.5; }
.final-card { background: var(--color-background-primary); border: 1.5px solid var(--color-border-info); border-radius: var(--border-radius-lg); padding: 1.25rem; margin-bottom: 1rem; }
.final-card .sec-header { margin-bottom: 10px; }
.output-block { background: var(--color-background-secondary); border-radius: var(--border-radius-md); padding: 12px 14px; font-family: var(--font-mono); font-size: 12px; color: var(--color-text-primary); line-height: 1.8; border: 0.5px solid var(--color-border-tertiary); margin-top: 10px; white-space: pre; }
.badge { font-size: 11px; padding: 3px 8px; border-radius: var(--border-radius-md); font-weight: 500; margin-left: auto; }
.hard { background: #FAECE7; color: #712B13; }
.med { background: #FAEEDA; color: #633806; }
.easy { background: #EAF3DE; color: #27500A; }
</style>

<div class="sheet">
<h2 class="sr-only">Smart City Planner — real problem sheet with given values and expected answers</h2>

<div class="brief">
  <h1>Smart City Planner — problem sheet</h1>
  <p>You are the lead engineer for a new city district called <strong style="color:var(--color-text-primary);font-weight:500;">Naya Nagar</strong> in Delhi. The municipal corporation has given you exact measurements and budgets. Use Python to answer every question below. All values are fixed — your output must match the expected answers.</p>
</div>

<div class="section">
  <div class="sec-header">
    <div class="sec-num s1">1</div>
    <div>
      <div class="sec-title">Land plot measurements</div>
      <div class="sec-subtitle">math.sqrt · math.pi · math.ceil · operators</div>
    </div>
    <span class="badge easy">Easy</span>
  </div>

  <div class="given-box">
    <div class="given-label">Given data</div>
    <div class="given-grid">
      <div class="given-item"><div class="val">120 m</div><div class="lbl">Park plot — circle radius</div></div>
      <div class="given-item"><div class="val">85 m × 200 m</div><div class="lbl">Commercial plot — rectangle</div></div>
      <div class="given-item"><div class="val">a=90, b=110, c=140 m</div><div class="lbl">Hospital plot — triangle sides</div></div>
      <div class="given-item"><div class="val">₹180 / metre</div><div class="lbl">Fencing cost per metre</div></div>
    </div>
  </div>

  <ul class="task-list">
    <li><span class="task-num">1.1</span>Calculate the area of the circular park using <span class="formula">math.pi * r ** 2</span>. Round to 2 decimal places.</li>
    <li><span class="task-num">1.2</span>Calculate the area of the rectangular commercial plot.</li>
    <li><span class="task-num">1.3</span>Calculate the area of the triangular hospital plot using Heron's formula: <span class="formula">s = (a+b+c)/2</span>, then <span class="formula">math.sqrt(s*(s-a)*(s-b)*(s-c))</span>. Round to 2 decimal places.</li>
    <li><span class="task-num">1.4</span>The perimeter of the circular park is <span class="formula">2 * math.pi * r</span>. Use <span class="formula">math.ceil()</span> on the perimeter before multiplying by ₹180 — because you must buy whole metres of fencing. Print the total fencing cost.</li>
    <li><span class="task-num">1.5</span>Write a function <span class="formula">classify_plot(area)</span>: area &lt; 5000 = "Small", 5000–20000 = "Medium", &gt;20000 = "Large". Classify all three plots.</li>
  </ul>

  <div class="expected">
    <div class="exp-label">Expected answers</div>
    <div class="exp-pill">Park area: 45238.93 m²</div>
    <div class="exp-pill">Commercial: 17000 m²</div>
    <div class="exp-pill">Hospital: 4879.30 m²</div>
    <div class="exp-pill">Fencing cost: ₹1,35,936</div>
    <div class="exp-pill">Park → Large, Commercial → Medium, Hospital → Small</div>
  </div>
</div>

<div class="section">
  <div class="sec-header">
    <div class="sec-num s2">2</div>
    <div>
      <div class="sec-title">Building specifications</div>
      <div class="sec-subtitle">math.pow · math.log · math.floor · math.ceil</div>
    </div>
    <span class="badge med">Medium</span>
  </div>

  <div class="given-box">
    <div class="given-label">Given data — three buildings to analyse</div>
    <div class="given-grid">
      <div class="given-item"><div class="val">Residential tower</div><div class="lbl">40m × 30m · 25 floors · concrete</div></div>
      <div class="given-item"><div class="val">Office block</div><div class="lbl">60m × 45m · 12 floors · steel</div></div>
      <div class="given-item"><div class="val">Community hall</div><div class="lbl">25m × 20m · 2 floors · wood</div></div>
      <div class="given-item"><div class="val">Floor height: 3.2 m</div><div class="lbl">Same for all buildings</div></div>
    </div>
  </div>

  <ul class="task-list">
    <li><span class="task-num">2.1</span>For each building, calculate total height = <span class="formula">floors * 3.2</span> and volume = <span class="formula">length * width * total_height</span>. Store results in a dictionary per building.</li>
    <li><span class="task-num">2.2</span>Elevators needed = <span class="formula">math.ceil(math.log(floors, 2))</span>, minimum 1. Calculate for each building.</li>
    <li><span class="task-num">2.3</span>Structural load in tonnes: densities are concrete = 2400, steel = 7800, wood = 600 (kg/m³). Use <span class="formula">math.pow(volume, 1) * density / 1000</span> then apply <span class="formula">math.floor()</span> to the result. Print load for each building.</li>
    <li><span class="task-num">2.4</span>Which building has the highest structural load? Print its name and the load value.</li>
  </ul>

  <div class="expected">
    <div class="exp-label">Expected answers</div>
    <div class="exp-pill">Residential: 96000 m³ · 5 elevators · 230,400 tonnes</div>
    <div class="exp-pill">Office: 103,680 m³ · 4 elevators · 808,704 tonnes</div>
    <div class="exp-pill">Community hall: 3,200 m³ · 1 elevator · 1,920 tonnes</div>
    <div class="exp-pill">Highest load: Office block</div>
  </div>
</div>

<div class="section">
  <div class="sec-header">
    <div class="sec-num s3">3</div>
    <div>
      <div class="sec-title">Solar energy system</div>
      <div class="sec-subtitle">math.cos · math.sin · math.radians · math.degrees · math.pow</div>
    </div>
    <span class="badge med">Medium</span>
  </div>

  <div class="given-box">
    <div class="given-label">Given data</div>
    <div class="given-grid">
      <div class="given-item"><div class="val">28.6°</div><div class="lbl">Delhi latitude</div></div>
      <div class="given-item"><div class="val">500 m²</div><div class="lbl">Rooftop panel area (residential)</div></div>
      <div class="given-item"><div class="val">800 m²</div><div class="lbl">Rooftop panel area (office)</div></div>
      <div class="given-item"><div class="val">18%</div><div class="lbl">Panel efficiency (0.18)</div></div>
      <div class="given-item"><div class="val">5.5 hrs</div><div class="lbl">Peak sun hours per day</div></div>
      <div class="given-item"><div class="val">₹8.50</div><div class="lbl">Cost per kWh saved</div></div>
    </div>
  </div>

  <ul class="task-list">
    <li><span class="task-num">3.1</span>Convert 28.6° to radians using <span class="formula">math.radians(28.6)</span>. Print the result.</li>
    <li><span class="task-num">3.2</span>Sun angle factor = <span class="formula">math.cos(math.radians(28.6))</span>. Daily output (kWh) = <span class="formula">area * 0.18 * sun_factor * 5.5</span>. Calculate for both rooftops.</li>
    <li><span class="task-num">3.3</span>Optimal tilt angle = <span class="formula">28.6 * 0.76 + 3.1</span> degrees. Convert this back to radians using <span class="formula">math.radians()</span>. Print both values.</li>
    <li><span class="task-num">3.4</span>Annual savings = <span class="formula">math.floor(daily_output * 365 * 8.5)</span>. Calculate for both buildings and print combined total savings.</li>
    <li><span class="task-num">3.5</span>Use <span class="formula">math.sin(math.radians(28.6))</span> to calculate the shadow length factor of a 10m tall panel mast: <span class="formula">shadow = 10 / math.tan(math.radians(28.6))</span>. Round to 2 decimal places.</li>
  </ul>

  <div class="expected">
    <div class="exp-label">Expected answers</div>
    <div class="exp-pill">Radians: 0.4992</div>
    <div class="exp-pill">Residential daily: 389.74 kWh</div>
    <div class="exp-pill">Office daily: 623.59 kWh</div>
    <div class="exp-pill">Optimal tilt: 24.836°</div>
    <div class="exp-pill">Combined annual savings: ₹31,08,175</div>
    <div class="exp-pill">Shadow length: 18.38 m</div>
  </div>
</div>

<div class="section">
  <div class="sec-header">
    <div class="sec-num s4">4</div>
    <div>
      <div class="sec-title">Population &amp; traffic simulation</div>
      <div class="sec-subtitle">random.randint · random.uniform · random.choice · random.seed</div>
    </div>
    <span class="badge med">Medium</span>
  </div>

  <div class="given-box">
    <div class="given-label">Given data — 4 zones</div>
    <div class="given-grid">
      <div class="given-item"><div class="val">Residential</div><div class="lbl">Area: 45238.93 m² (from Q1.1)</div></div>
      <div class="given-item"><div class="val">Commercial</div><div class="lbl">Area: 17000 m² (from Q1.2)</div></div>
      <div class="given-item"><div class="val">Hospital</div><div class="lbl">Area: 4879.30 m² (from Q1.3)</div></div>
      <div class="given-item"><div class="val">Industrial</div><div class="lbl">Area: 30000 m² (fixed)</div></div>
    </div>
  </div>

  <ul class="task-list">
    <li><span class="task-num">4.1</span>Set <span class="formula">random.seed(42)</span> at the top of this section so your results are reproducible.</li>
    <li><span class="task-num">4.2</span>For each zone, generate a random density using <span class="formula">random.randint(50, 200)</span>. Population = <span class="formula">math.floor(area * density / 1000)</span> (per 1000 m²). Store each zone as a dict with keys: zone, area, density, population.</li>
    <li><span class="task-num">4.3</span>For each zone: peak vehicles = <span class="formula">math.floor(population * random.uniform(0.3, 0.6))</span>, off-peak = <span class="formula">math.floor(population * random.uniform(0.05, 0.15))</span>. Also pick a road condition from <span class="formula">['Good', 'Average', 'Poor']</span> using <span class="formula">random.choice()</span>.</li>
    <li><span class="task-num">4.4</span>Write <span class="formula">suggest_lanes(peak_vehicles)</span>: &lt;500→2 lanes, 500–1500→4 lanes, 1500–3000→6 lanes, &gt;3000→8 lanes + flyover. Print suggestion for each zone.</li>
  </ul>
  <div class="warn">Important: use <span class="formula">random.seed(42)</span> before any random call in this section. This locks your random numbers so they are predictable and testable.</div>
</div>

<div class="section">
  <div class="sec-header">
    <div class="sec-num s5">5</div>
    <div>
      <div class="sec-title">City statistics engine</div>
      <div class="sec-subtitle">math.sqrt · math.log · all previous data combined</div>
    </div>
    <span class="badge hard">Hard</span>
  </div>

  <div class="given-box">
    <div class="given-label">Use all values computed in sections 1–4</div>
    <div class="given-grid">
      <div class="given-item"><div class="val">4 zones</div><div class="lbl">From section 4</div></div>
      <div class="given-item"><div class="val">3 buildings</div><div class="lbl">From section 2</div></div>
      <div class="given-item"><div class="val">2 solar rooftops</div><div class="lbl">From section 3</div></div>
    </div>
  </div>

  <ul class="task-list">
    <li><span class="task-num">5.1</span>Write <span class="formula">population_stats(zones)</span>. From your list of zone dicts, calculate: total population, average population, std deviation using <span class="formula">math.sqrt(variance)</span> where variance = mean of squared differences from the mean.</li>
    <li><span class="task-num">5.2</span>Calculate total structural load across all 3 buildings (sum from section 2). Express it in millions of tonnes using <span class="formula">round(total / 1_000_000, 2)</span>.</li>
    <li><span class="task-num">5.3</span>Naya Nagar's "green score" = <span class="formula">math.log(park_area / total_city_area * 100 + 1, 10) * 50</span>. Total city area = sum of all 4 zone areas. Round to 1 decimal place. A score &gt; 20 is "Eco-Friendly".</li>
    <li><span class="task-num">5.4</span>Write <span class="formula">generate_city_report()</span> that prints a clean summary: city name, total population, total building load in million tonnes, combined daily solar output, green score and rating, and a recommendation line.</li>
  </ul>

  <div class="output-block">===== NAYA NAGAR CITY REPORT =====
Total population     : ????
Total building load  : ???? million tonnes
Daily solar output   : ???? kWh
Green score          : ???? — Eco-Friendly / Needs Work
Recommendation       : ????
==================================</div>
</div>

<div class="final-card">
  <div class="sec-header">
    <div class="sec-num" style="background:#E6F1FB;color:#0C447C;">F</div>
    <div>
      <div class="sec-title">Final constraint checklist</div>
    </div>
  </div>
  <ul class="task-list">
    <li><span class="task-num">R1</span>Only <span class="formula">import math</span> and <span class="formula">import random</span> — no other imports</li>
    <li><span class="task-num">R2</span>Every function must return a value — never return None silently</li>
    <li><span class="task-num">R3</span>Use <span class="formula">math.sqrt</span>, <span class="formula">math.pow</span>, <span class="formula">math.floor</span>, <span class="formula">math.ceil</span>, <span class="formula">math.pi</span>, <span class="formula">math.log</span>, <span class="formula">math.radians</span>, <span class="formula">math.cos</span>, <span class="formula">math.sin</span> — all nine must appear at least once</li>
    <li><span class="task-num">R4</span>Use <span class="formula">random.randint</span>, <span class="formula">random.uniform</span>, <span class="formula">random.choice</span>, <span class="formula">random.seed</span> — all four must appear</li>
    <li><span class="task-num">R5</span>Section 4 must start with <span class="formula">random.seed(42)</span> — non-negotiable</li>
    <li><span class="task-num">R6</span>All currency output must be formatted as ₹X,XX,XXX — use Python string formatting</li>
  </ul>
</div>

</div>