How many windows are in New York City?

The failure mode is a single multiplier applied to population, no scope question asked, and no acknowledgment that NYC’s building mix is structurally unlike any other US city. In 2026, interviewers at AI-native companies use this question as a decomposition and communication test, not an arithmetic test. An LLM can compute the arithmetic. What they’re scoring is whether you notice that the problem contains genuine segments that behave differently, and whether you can communicate uncertainty without freezing.

Scope question first

Before any numbers: “Are we counting windows on buildings only, or also vehicles? Registered cars in NYC add roughly 15 million windows on their own. I’ll assume buildings only for now and can layer in vehicles if useful.”

Asking this before calculating signals exactly the instinct that carries into real product work: scope before solution.

Why NYC is harder than a generic US city

Three structural facts about NYC that a candidate must name to score well:

No detached single-family homes. Only 8% of NYC housing units are 1-unit detached structures. A generic US decomposition (population / 2.5 = households, times 10 windows each) assumes something like 35 to 40% single-family, which is wildly wrong for NYC. Applying it here understates high-rise density and overstates ground-floor residential surface area.

NYC has 3.7 million housing units, and 62% are in buildings of 6 or more units. Nearly half (49%) are in buildings of 20 or more units. This concentration makes the per-unit window count much lower than suburban housing (no front/back facades to yourself) and makes the building-level count much higher.

Glass curtain-wall skyscrapers have no discrete windows. The Seagram Building, One World Trade, and several hundred other Manhattan towers use a continuous glass facade where the entire skin is the window. Treating these like a mid-century apartment building with punched openings is architecturally wrong. The insight is worth naming: for those buildings, you estimate by facade area, not window count.

The decomposition

State the structure: residential (segmented by building type) plus commercial (segmented by size and facade type). NYC has roughly 1 million total buildings, which anchors the final sanity check.

Residential. NYC has approximately 3.7 million housing units.

• Low-rise (1 to 5 stories, outer-borough walk-ups and row houses): roughly 35% of units, about 1.3 million. Average 5 to 6 windows per unit due to shared walls. Total: 1.3M x 5.5 = ~7.2M windows.
• Mid-rise (6 to 20 floors, prewar and postwar multifamily): roughly 30% of units, about 1.1 million. Average 7 to 8 windows per unit (one exterior-facing side, one to two other exposures). Total: 1.1M x 7.5 = ~8.3M windows.
• High-rise (20+ floors): roughly 35% of units, about 1.3 million. Average 6 windows per unit (fewer exposed walls per unit as the tower narrows). Total: 1.3M x 6 = ~7.8M windows.

Residential total: roughly 23 million windows.

Commercial. NYC has 7,000 high-rises above 115 feet and over 320 skyscrapers. Segment by facade type:

• Glass curtain-wall towers (approximately 400 large buildings): estimate by facade area. A 40-story office tower with a 100-foot square footprint has 4 sides x 100 ft wide x 600 ft tall = 240,000 sq ft of glass. At one window-equivalent per 15 sq ft: about 16,000 window-equivalents per tower. 400 x 16,000 = 6.4M. (This is the insight moment: scale is governed by facade geometry, not room count.)
• Mid-scale office, retail, and mixed-use buildings (roughly 50,000 buildings): average 20 windows each. 50,000 x 20 = 1M.
• Small storefront commercial and mixed-use (roughly 150,000 buildings): average 4 to 5 windows each. 150,000 x 4.5 = 675K.

Commercial total: roughly 8 million windows.

Building total: 23M + 8M = approximately 31 million windows, range 28 to 35 million.

Sanity check

NYC has roughly 1 million buildings. 31 million windows divided by 1 million buildings is 31 windows per building on average. That is consistent with a city where most structures are multi-unit residential or commercial with multiple stories, not single-family homes. The average feels right: a 10-unit walk-up with 6 windows per unit is already 60 windows; a 200-unit high-rise with 6 windows per unit is 1,200. Averaging these against small storefronts, the city-wide mean landing around 31 is defensible.

If you include vehicles: NYC has about 2.5 million registered passenger vehicles at 6 windows each (2 front, 2 rear, 2 side) plus roughly 5,800 MTA buses and 6,400 subway cars. Vehicles add roughly 15 to 16 million, bringing the total to approximately 45 to 50 million.

What the interviewer actually scores

In 2026, the arithmetic is not the test. The scorecard, in order:

1. Scope clarification before starting (vehicles or buildings only?).
2. Stated decomposition tree before any numbers (residential segmented by building type, commercial segmented by facade type).
3. NYC-specific insight: the city skews heavily multifamily, has no meaningful single-family base, and its tallest buildings use curtain-wall glass where window counts are replaced by facade area.
4. Named assumptions with rationale, especially the pivotal ones (window count per unit by tier, curtain-wall coverage fraction).
5. Ranged final answer, not a false-precision single number.
6. Stated validation step: what data would you check to tighten the estimate?

The PM skill underneath

Segmenting a problem that looks homogeneous on the surface. NYC windows appears to be a single category. It contains at least three meaningfully different residential segments and two commercial segments with different estimation logic. This is structurally identical to the PM task of segmenting users who look like “enterprise customers” into several cohorts with different willingness to pay, churn risk, and feature needs. The candidate who flattens the NYC housing stock into one multiplier is the same PM who ships one product for all “enterprise” accounts and wonders why the metrics are noisy. The curtain-wall insight is the signal that separates genuine domain thinking from a memorized Fermi template.