Oct 08, 2026 by Offer

Brain teaser: light bulbs (With Examples): Interview Answer Guide 2027

In the light bulbs puzzle, person n toggles every nth bulb of 100. The bulbs left on are the perfect squares — 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — so 10 stay lit. This brain teaser interview question works because each bulb is toggled once per divisor, and only perfect squares have an odd divisor count.

What the Brain Teaser Interview Question Tests

Whether you can translate a story into math: toggles correspond to divisors of the bulb number.
Whether you spot the parity insight — on/off is just odd/even toggle count.
Whether you finish cleanly: perfect squares up to 100, counted correctly as 10.

How to Answer the Brain Teaser Interview Question

Show the pattern with concrete small cases before generalizing:

Example — the first 6 bulbs. Bulb 1: divisors {1} → 1 toggle → on. Bulb 2: {1,2} → off. Bulb 3: {1,3} → off. Bulb 4: {1,2,4} → on. Bulb 5: {1,5} → off. Bulb 6: {1,2,3,6} → off.
Spot it. Only bulbs 1 and 4 are on — both perfect squares.
Scale up. The same logic holds to 100: squares 1²–10² stay on, everything else ends off. Answer: 10 bulbs.
Bonus variant. With n bulbs, exactly ⌊√n⌋ stay on — e.g., 7 bulbs → bulbs 1 and 4.

Sample close: "Working small cases first is the whole technique — the pattern jumps out by bulb 4."

Common Mistakes With the Brain Teaser Interview Question

Simulating all 100 bulbs by hand. Interviewers want the divisor insight, not brute force.
Saying 'even numbers' or 'multiples' without the parity argument — the answer needs the odd-divisor reasoning.
Miscounting the squares: there are 10 perfect squares up to 100, not 9 (don't forget 100 = 10²).

Brain teasers are not about the answer — interviewers have heard it. They are about watching you reason from scratch. Narrate the divisor insight as you discover it and you pass; recite a memorized answer with no reasoning and you fail the real test.

Keep Reading

FAQ

What is the answer to the 100 light bulbs puzzle?

10 bulbs stay on: numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. These are the perfect squares, the only numbers with an odd count of divisors.

Why do only perfect squares stay on?

Each bulb is toggled once per divisor. Divisors pair up (e.g., 2×6 for 12) except when a number is a square — then one divisor pairs with itself, leaving an odd count, so the bulb ends on.

Is there a second light bulb interview puzzle?

Yes — the famous three-switches-one-bulb variant: flip switch 1 on, wait, turn it off, flip switch 2 on, then check whether the bulb is on, off-but-warm, or off-and-cold.

Do brain teasers still appear in interviews?

Less often than a decade ago, but trading firms and some tech companies still use them to test structured reasoning under pressure.

Preparing for Citadel's interview? Our 2027 Citadel Online Assessment and Coding Challenge Tutorials has practice questions and answers — $79 one-time, instant download.