The Brain Teaser Dilemma: A Comprehensive Guide to Theory, Strategy, and Solution for the Modern
Interview
A deep dive into why brain teaser questions are used, how to solve them, and whether they still
matter in today's hiring landscape.
Section 1: Introduction to Brain Teaser Questions
This section establishes the foundational knowledge required to understand the role and context of
brain teasers in the professional world. It defines the concept, traces its historical evolution as
an interview tool, and outlines the rationale behind its use, setting the stage for a deeper
analysis of its efficacy and modern relevance.
1.1 Defining the Brain Teaser: Beyond Puzzles and Riddles
Brain teaser interview questions are puzzles or logic problems presented during job interviews to
assess a candidate's cognitive and analytical capabilities. Unlike traditional interview questions
that probe a candidate's experience or knowledge, brain teasers are designed to evaluate a distinct
set of skills, including problem-solving, critical thinking, creativity, and the ability to approach
challenges from unconventional angles. You can see some common examples here. They are defined by their abstract
nature; they are deliberately not set within a business context, which allows interviewers to
observe how applicants apply logic and creativity outside their specific areas of expertise. These
questions are a core part of modern skill tests for career advancement.
The core purpose of these questions is not necessarily to elicit a single correct answer. In many
cases, particularly with estimation or situational puzzles, the final answer is irrelevant. Instead,
the interviewer's primary interest lies in the candidate's approach—the logical framework they
construct, the assumptions they make, and their ability to articulate their thought process under
pressure. These questions are intended to reveal a candidate's mental agility and stress management
skills in a way that questions with rehearsed answers cannot. They aim to provide a window into core
competencies such as analytical skills, quantitative aptitude, stress tolerance, and communication,
all of which are deemed critical in high-stakes professional environments.
1.2 A Historical Perspective: From Corporate Giants to the Tech Boom
The use of brain teasers as a formal interview tool is not a recent phenomenon. Their history in the
corporate world dates back to the 1950s and 1960s, when industrial giants like IBM and AT&T
popularized them. The underlying philosophy was that presenting candidates with unexpected and
abstract problems could offer valuable insights into how they would perform when faced with
real-world challenges that lacked clear precedents.
This practice gained widespread notoriety and became a cultural touchstone during the technology boom
of the late 20th and early 21st centuries. Companies like Microsoft and, most famously, Google,
became legendary for posing esoteric questions to prospective employees. The question, "Why are
manhole covers round?" is a classic example from this era, attributed to Microsoft, and has since
become one of the most well-known brain teasers. The rationale for this
method was deeply rooted in the belief that it could simulate the high-pressure, ambiguous
problem-solving environment that defined the fast-paced tech industry, thereby helping to
distinguish top-tier candidates from the rest of the pool.
1.3 The Stated Rationale vs. The Modern Reality
The official purpose of brain teaser questions is to provide a standardized method for gauging a
candidate's raw intellectual horsepower. By presenting novel problems, employers aim to assess
mental agility, stress management, and on-the-spot problem-solving abilities, bypassing the
polished, memorized answers that often populate traditional interviews.
However, this stated rationale is now at the center of a significant debate within the fields of
human resources and industrial-organizational psychology. A growing body of evidence, supported by
expert testimony from industry leaders, casts serious doubt on the effectiveness of these questions.
Many of the very companies that popularized them, including Google, have publicly disavowed their
use, citing internal data that found them to be a "complete waste of time" with no predictive value
for job performance.
Despite this high-profile abandonment and mounting criticism, the practice persists in many sectors.
This discrepancy points to a powerful inertia within corporate recruiting practices. The continued
use of brain teasers suggests that hiring methodologies are often driven by tradition and anecdotal
belief—the "it's how we've always done it" mentality—rather than by empirical validation.
Interviewers who were once subjected to these questions may perpetuate the cycle, believing it to be
an effective filter simply because it was part of their own selection process. This reveals a
systemic resistance to data-driven change within the hiring landscape. Consequently, candidates must
continue to prepare for these questions, not because they are a universally effective assessment
tool, but because they remain a persistent, if sometimes irrational, feature of the modern
interview.
Section 2: A Taxonomy of Brain Teaser Questions
Brain teaser questions are not a monolithic category; they encompass a wide variety of puzzle types,
each designed to test a slightly different facet of a candidate's cognitive skill set. Understanding
this taxonomy is the first step for a candidate to identify the nature of the challenge and deploy
the appropriate problem-solving strategy. The following table provides a high-level overview of the
primary categories.
| Brain Teaser Category |
Primary Skills Assessed |
Classic Example |
| Guesstimation & Market Sizing |
Structured thinking, quantitative reasoning, logical assumption-making,
numeracy |
"How many piano tuners are there in New York City?" |
| Logical & Deductive Reasoning |
Systematic problem-solving, process of elimination, inference,
structured thinking |
"You have three light bulbs in a room and three switches outside. Which
switch controls which bulb?" |
| Mathematical & Quantitative |
Numeracy, quantitative problem-solving, probability, algebraic framing
|
"Using a 5-gallon jug and a 3-gallon jug, how do you measure exactly 4
gallons of water?" |
| Lateral Thinking & "Out-of-the-Box" |
Creativity, flexible thinking, ability to reframe problems and
challenge assumptions |
"You are shrunk to the size of a nickel and thrown into a blender. What
do you do?" |
| Wordplay, Illusion, & Trick Questions |
Active listening, attention to detail, identifying misdirection,
cognitive flexibility |
"A farmer has 17 sheep and all but 9 die. How many are left?" |
| Pattern Recognition |
Analytical observation, inductive reasoning, data analysis, sequential
logic |
"What is the next number in the sequence: 1, 3, 6, 10, 15, …?" |
2.1 Guesstimation & Market Sizing Questions
Definition: These questions require candidates to produce a reasonable estimate for
a quantity that is not readily available, often concerning the size of a market or the number of a
specific item within a defined area. They are characterized by a lack of concrete data, forcing the
candidate to build a solution from logical assumptions.
Skills Assessed: The primary skill evaluated is structured thinking, specifically
the ability to break down an impossibly large question into a series of manageable, logical steps.
This includes making and justifying assumptions, demonstrating quantitative aptitude, and clearly
communicating the estimation process. The interviewer explicitly values the candidate's methodology
over the precision of the final number.
Examples:
- "How many piano tuners are there in the entire world?"
- "How many square feet of pizza are eaten in the United States each month?"
- "How many golf balls can fit in a Boeing 737?"
- "How many gas stations are in the U.S.?"
2.2 Logical & Deductive Reasoning Puzzles
Definition: These are scenarios that can be solved through the systematic
application of pure deductive reasoning, process of elimination, and structured thinking. They
typically present a set of constraints and require the candidate to find the single correct solution
that satisfies all conditions, often without relying on tricks or ambiguity.
Skills Assessed: These puzzles directly test systematic problem-solving, inference,
and the ability to deconstruct a complex problem into its constituent parts.
Examples:
- The Three Light Switches: You are outside a room with three light switches, each
corresponding to one of three light bulbs inside. You can manipulate the switches as you wish,
but you may only enter the room once. How do you determine which switch controls which bulb?
- The River Crossing: A farmer needs to cross a river with a fox, a chicken, and
a sack of corn. The boat can only hold the farmer and one other item. The fox cannot be left
alone with the chicken, and the chicken cannot be left alone with the corn. How does everyone
get across?
- Incorrectly Labeled Bags: You have three bags, one with only apples, one with
only oranges, and one with a mix of both. Every bag is labeled incorrectly. You are allowed to
pick only one fruit from one bag. Which bag do you choose from to correctly label all three?
2.3 Mathematical & Quantitative Problems
Definition: These are puzzles grounded in mathematical concepts, ranging from basic
algebra and ratios to more complex probability theory. They require a direct application of
quantitative skills to arrive at a definitive answer.
Skills Assessed: These questions directly test numeracy, the ability to frame a
problem in mathematical terms, and the speed and accuracy of mental calculations.
Examples:
- The Water Jug Problem: You have a 5-gallon jug and a 3-gallon jug, and an
unlimited supply of water. How can you measure out exactly 4 gallons?
- The Burning Ropes: You have two ropes, each of which takes exactly one hour to
burn from end to end. The ropes do not burn at a uniform rate. How can you measure exactly 45
minutes?
- Cats and Mice: If five cats can catch five mice in five minutes, how many cats
are needed to catch 100 mice in 100 minutes?
2.4 Lateral Thinking & "Out-of-the-Box" Riddles
Definition: These puzzles present scenarios that seem bizarre, impossible, or
paradoxical. The solution requires the candidate to think creatively and challenge the implicit
assumptions or constraints of the problem statement. This is often referred to as lateral thinking.
Skills Assessed: The primary skills tested are creativity, cognitive flexibility,
and the ability to reframe a problem. The interviewer is looking for innovative approaches rather
than a purely linear, logical deduction.
Examples:
- The Baseball Game: A man leaves home, makes three left turns, and returns home
to find two men in masks waiting for him. Who are they?
- Moving Mount Fuji: How would you move Mount Fuji?
- Shrunk in a Blender: You are shrunk to the size of a nickel and thrown into an
empty blender. The blades will start in 60 seconds. What do you do?
2.5 Wordplay, Illusion, and Trick Questions
Definition: These questions are specifically designed to mislead the listener
through clever wording, ambiguous phrases, or by focusing attention on irrelevant details to obscure
a simple answer. They are a direct test of active listening and attention to detail.
Skills Assessed: The key skills are close listening, the ability to identify
misdirection, and cognitive flexibility to overcome the initial, incorrect interpretation.
Examples:
- The Farmer's Sheep: A farmer has 17 sheep, and all but 9 die. How many are
left?
- Marrying the Widow's Sister: Is it possible for a man in California to marry
his widow's sister?
- Two Coins: Two U.S. coins add up to 30 cents. If one of them is not a nickel,
what are the two coins?
- Most Letters: What two words, when combined, hold the most letters?
2.6 Pattern Recognition Challenges
Definition: These problems present a sequence of numbers, letters, symbols, or
shapes and require the candidate to discern the underlying logical pattern to predict the next
element or fill in a missing one.
Skills Assessed: These questions test analytical observation, inductive reasoning,
and the ability to spot trends in data, which is a foundational skill in data analysis and modeling,
often relying on understanding sorting algorithms or array data structures.
Examples:
- Triangular Numbers: What is the next number in the sequence: 1, 3, 6, 10, 15,
…?
- Jumbled Letters: Rearrange the letters in "NEW DOOR" to form one word.
- Interleaved Sequences: What is the next number in the sequence: 0 0 1 2 2 4 3
6 4 8 5?
Section 3: A Strategic Framework for Deconstruction and Response
Successfully navigating a brain teaser in a high-stakes interview is less about innate genius and
more about employing a disciplined, strategic approach. This section provides a universal framework
that candidates can adapt to any type of puzzle, transforming a stressful challenge into an
opportunity to showcase key professional competencies.
3.1 The Foundational Mindset: Calm, Clarify, Communicate
Before any analytical work begins, a candidate's success is predicated on adopting the right mindset.
Three core principles should guide the initial response.
- Stay Calm: Brain teasers are intentionally designed to be challenging and, at
times, stressful. The initial reaction of panic or feeling flustered is common but
counterproductive. The first and most critical action is to take a moment to breathe and compose
oneself. This simple act demonstrates composure under pressure, a key competency that
interviewers are actively assessing. Rushing to an answer is the most frequent pitfall and often
leads to falling for the puzzle's intended trick.
- Clarify the Question: A candidate should never assume they have a complete
understanding of the problem's constraints. Asking intelligent, clarifying questions is a sign of critical thinking and
diligence, not a sign of weakness. This step serves two purposes: it ensures the candidate is
solving the correct problem, and it can often simplify the task by narrowing its scope. For
instance, when asked, "How many golf balls can fit in a school bus?" a candidate should probe
for details: "Are we assuming a standard full-size school bus, or a shorter one? Are the seats
still inside, or has it been gutted?".
- Communicate Your Process (The "Think Aloud" Protocol): This is the single most
important strategy in answering a brain teaser. The interviewer is fundamentally more interested
in how a candidate thinks than in the final numerical answer. By verbalizing their thought
process—stating assumptions, outlining the plan, walking through calculations, and performing
sanity checks—the candidate turns the puzzle from a test of knowledge into a live demonstration
of their analytical and communication skills.
3.2 A Universal Step-by-Step Approach
While specific techniques vary by puzzle type, a universal, structured approach can be applied to
nearly any brain teaser. An adaptation of the STAR method, commonly used for behavioral questions,
provides a robust framework.
- Structure Your Approach: Before diving into the details, provide the
interviewer with a roadmap of how you intend to solve the problem. This demonstrates
organizational skills and allows the interviewer to follow your logic more easily. For example:
"Okay, to solve this, I'm going to proceed in three steps. First, I'll state my key assumptions.
Second, I'll break the problem down into its core components. Finally, I'll perform the
necessary calculations and conclude with a sanity check of the result."
- Think Aloud and State Assumptions: As you execute your plan, narrate every step.
If you are solving a guesstimation problem, clearly state every assumption you make and provide
a brief justification. For example: "I'm going to assume the population of New York City is
approximately 8 million people. This is a commonly cited figure and provides a solid starting
point." This transparency is crucial for the interviewer to evaluate your reasoning.
- Ask Clarifying Questions: As you proceed, continue to engage the interviewer.
If you encounter a point of ambiguity or need to make a significant assumption, you can check
in: "To estimate the number of windows per commercial building, I'm going to assume an average
of 100 windows. Does that seem like a reasonable starting point to you?". This makes the process
more collaborative and shows you are adaptable.
- Resolve Systematically: Deconstruct the problem into smaller, more manageable
parts. For guesstimates, this involves segmenting a population or breaking down a volume into
smaller units. For logic puzzles, it means addressing one constraint at a time to methodically
eliminate possibilities. This systematic resolution is the core of the analytical demonstration.
3.3 Specialized Techniques for Different Categories
While the universal framework applies broadly, certain puzzle categories benefit from specialized
techniques.
- For Guesstimates: A key decision is whether to use a top-down or bottom-up
approach. A top-down approach starts with a large, known number (e.g., the population of the
U.S.) and uses assumptions to narrow it down. A bottom-up approach starts with a single unit
(e.g., one gas station's customer base) and multiplies upward to reach the total. The choice
should be explained and justified based on the problem.
- For Logic Puzzles: The most effective techniques include the elimination method
(ruling out incorrect possibilities), backsolving (working backward from the desired outcome to
find the necessary steps), and testing small cases (solving a simpler version of the problem to
identify a pattern). Using a pen and paper to visualize the problem, such as drawing the jugs or
the river, is highly recommended to keep track of complex steps.
- For Lateral Thinking & Wordplay: The primary technique is to actively
challenge the most obvious interpretation of the question. Go through the phrasing word by word,
looking for double meanings, hidden puns, or false assumptions embedded in the language.
3.4 Common Pitfalls and How to Avoid Them
Candidates often stumble not due to a lack of intelligence, but by falling into predictable traps.
- Rushing to an Answer: This is the most common error. It demonstrates a lack of
a thoughtful process and makes the candidate vulnerable to the puzzle's tricks. The solution is
to consciously pause before speaking.
- Staying Silent: When a candidate gets stuck, the worst possible response is
silence. This is often interpreted as giving up. It is far better to articulate the roadblock:
"I've established X and Y, but I'm currently stuck on how to connect them. I'm considering if
there's a constraint I'm overlooking." This still demonstrates a thinking process.
- Overcomplicating the Problem: Some brain teasers have deceptively simple
answers. If a solution becomes excessively convoluted, it is wise to pause and ask, "Is there a
simpler way to frame this problem that I might be missing?".
- Ignoring or Hiding Assumptions: Failing to explicitly state the assumptions
being made is a critical error. The interviewer cannot follow or evaluate a candidate's logic if
they do not know the premises upon which it is built.
Section 4: The Great Debate: Efficacy, Validity, and Bias
While brain teasers persist as an interview tool, their use is highly contentious. A significant
body of research and expert opinion from within the industries that once championed them now
questions their fundamental value as an assessment tool. This section provides a critical,
evidence-based evaluation of the brain teaser, examining its predictive validity, the psychological
dynamics it creates, and its potential to introduce bias into the hiring process.
4.1 The Validity Question: Do Brain Teasers Predict Job Performance?
The central argument against the use of brain teasers is their lack of predictive validity—that is,
the inability of a candidate's performance on a puzzle to predict their future performance on the
job. The most prominent critic is Google, a company that, after extensive internal data analysis,
concluded that brain teasers are a "complete waste of time". Laszlo Bock, Google's former Senior
Vice President of People Operations, stated unequivocally that "they don't predict anything". This
conclusion, coming from a data-driven organization that once epitomized the brain teaser interview,
carries significant weight.
Research in industrial-organizational psychology supports this view. While general cognitive
ability has been consistently shown to be one of the best predictors of job performance across
various roles and industries, brain teasers are considered a poor and unreliable proxy for this ability. They test a very narrow
and specific skill: solving an abstract, decontextualized problem under acute pressure. There is
little evidence to suggest that this skill transfers effectively to the complex, multifaceted, and
context-dependent problems encountered in a typical professional role. In contrast, assessment
tools with higher predictive validity, such as structured behavioral interviews ("Tell me about a
time when...") and work-sample tests, are now favored by companies like Google that have moved
toward more evidence-based hiring practices.
4.2 The Interviewer Effect: Cognitive Biases and Dark Motives
Beyond their questionable validity, a more troubling critique of brain teasers focuses on the
psychological dynamics of the interview itself. A recurring theme in discussions among hiring
professionals is that these questions often serve primarily to make the interviewer feel
intelligent and powerful. When an assessment tool's main effect is psychological validation for the
person administering it rather than an accurate evaluation of the candidate, its integrity is
fundamentally compromised.
This observation is bolstered by academic research that has linked the elective use of brain
teasers to "dark personality traits" in interviewers, specifically narcissism and sadism. Such
individuals may derive satisfaction from the power imbalance inherent in the interview and enjoy
placing candidates in an uncomfortable and unsettling position. This transforms the interview from a
good-faith assessment of a candidate's skills into a psychological game that serves the
interviewer's ego. This dynamic fundamentally undermines the fairness and objectivity of the hiring
process, suggesting that in some cases, the use of brain teasers may be a symptom of a poorly
trained or even malicious interviewer.
4.3 The Candidate Experience: Fairness, Anxiety, and Organizational Perception
The use of brain teasers has a demonstrably negative impact on the candidate experience. Research
has shown that both job applicants and hiring managers tend to dislike these questions, rating them
as significantly less fair and more frustrating than traditional behavioral or situational
questions. This frustration stems from their perceived lack of job-relatedness.
These questions are known to induce unnecessary stress and anxiety, which can cause highly
qualified candidates to underperform during the interview. Furthermore, a candidate's interview
experience is a powerful signal about the company's culture. The use of questions that seem
arbitrary, aggressive, or designed to trip people up can lead candidates to infer that the work
environment is similarly toxic or unsupportive. In a competitive talent market, a negative
candidate experience can be a significant liability, deterring top applicants from accepting an
offer or even completing the interview process.
4.4 The Bias Minefield: How Puzzles Can Discriminate
Perhaps the most serious indictment against brain teasers is their potential to act as a vehicle for
unconscious bias. These puzzles are not culturally or cognitively neutral; their solutions often
depend on challenging specific assumptions and mental models (schemas) that are shaped by an
individual's background, including their gender, culture, and life experiences.
The classic "surgeon riddle" serves as a powerful illustration. The riddle states: "A father and son
are in a horrible car crash that kills the father. The son is rushed to the hospital; just as he’s
about to go under the knife, the surgeon says, 'I can’t operate—that boy is my son!'" A surprising
majority of people, including highly educated students at Boston University, fail to solve this
riddle because of a deeply ingrained gender schema that unconsciously associates the role of
"surgeon" with "male". The correct answer is that the surgeon is the boy's mother. The failure to
arrive at this solution is not an indicator of poor logical reasoning but rather a reflection of
pervasive societal gender bias.
Similarly, many other riddles and puzzles prey on common cognitive biases, such as confirmation
bias (the tendency to favor information that confirms existing beliefs), the anchoring effect
(relying too heavily on the first piece of information offered), and other flawed mental shortcuts
or heuristics. By using these questions, interviewers risk inadvertently selecting for candidates
whose cognitive frameworks and cultural assumptions align with their own, rather than for
candidates with the strongest objective problem-solving skills. This poses a significant threat to
diversity and inclusion efforts, as it may systematically disadvantage candidates from different
backgrounds whose life experiences have shaped different mental models.
Section 5: The Modern Landscape: Where Brain Teasers Still Thrive (And Why)
Despite the compelling arguments against their use, brain teaser questions have not disappeared from
the interview landscape. Their application has become polarized, with certain industries staunchly
defending their utility while others have led the charge in abandoning them. This schism reflects
differing philosophies on what constitutes a valuable predictive signal in the hiring process.
5.1 The Holdouts: Management Consulting and Quantitative Finance
The sectors that most notably continue to employ brain teasers are management consulting and
quantitative finance. Top-tier consulting firms like McKinsey, BCG, and Bain, as well as
quantitative trading firms and hedge funds, have historically integrated these questions into their
rigorous interview processes. Many consulting prep guides still focus on them.
The rationale in these fields is that the core work directly mirrors the skills tested by brain
teasers. Consultants and quants are constantly required to tackle ambiguous, high-pressure problems
with incomplete or novel data sets. From this perspective, a brain teaser is not an abstract puzzle
but a direct simulation of a core job competency: the ability to structure an unstructured problem,
make logical assumptions, remain composed under pressure, and clearly communicate a complex
analytical process. In these industries, the demonstration of structured thinking, mental agility,
and grace under fire is often considered as valuable as technical knowledge itself.
However, it is important to note a nuanced trend even within these holdout industries. Many consulting firms are reducing their reliance on classic riddles
and logic puzzles in favor of more business-relevant "guesstimate" or market-sizing questions,
which are seen as a bridge between abstract brain teasers and full-fledged consulting case studies. While their use is declining overall,
they remain "fair game," particularly at Tier 2 and Tier 3 consulting firms, which may use them
more frequently than the top MBB (McKinsey, Bain, BCG) firms.
5.2 The Pioneers of Change: The Tech Industry's Pivot
In stark contrast, the technology industry, once the most famous proponent of the brain teaser, has
been at the forefront of its decline. The case of Google is the most definitive example. As a
company driven by data analytics, Google turned its analytical lens inward to its own hiring
practices and found no correlation between a candidate's ability to solve brain teasers and their
subsequent job performance.
Based on this data, Google and many other leading tech companies have systematically phased out
these questions. They have pivoted towards assessment methods with proven predictive validity,
primarily structured behavioral and hypothetical questions. Questions like, "Tell me about a time
you had to manage a team to achieve a difficult goal," are now standard. These questions are
considered more difficult to "game" or prepare for with rote memorization and are believed to
provide a more authentic signal of a candidate's past behaviors and future potential. This pivot
represents a broader shift in modern human resources toward evidence-based hiring—a movement that
prioritizes methodologies validated by data over those sustained by tradition or an interviewer's
gut feeling.
Section 6: Comprehensive Brain Teaser Compendium with Detailed Solutions
This section provides a practical and detailed bank of common brain teaser questions, categorized
according to the taxonomy outlined in Section 2. Each entry includes the question, a discussion of
common pitfalls, and a model step-by-step solution that explicitly demonstrates the strategic
frameworks from Section 3. The goal is not to provide answers for memorization, but to illustrate
the application of a structured, communicative problem-solving process. You can find more brain teaser examples online.
6.1 Guesstimation & Market Sizing
Question: "How many piano tuners are there in New York City?"
Common Pitfall: Freezing up due to the seemingly impossible nature of the
question, or getting bogged down in trying to find exact, un-knowable figures instead of
focusing on a logical estimation process.
Detailed Solution:
Calm & Clarify: "That's an interesting question. To make
sure I'm solving for the right scope, are we defining 'New York City' as all five
boroughs? And are we considering only full-time, professional piano tuners?" (Interviewer
confirms: Yes, five boroughs, full-time professionals).
Structure & Think Aloud: "Great. I'll approach this by
estimating the total demand for piano tuning and then the total supply one tuner can
provide. I'll use a top-down approach for demand. My plan is:
- Estimate the population of NYC.
- Estimate the number of households.
- Estimate the percentage of households with a piano.
- Estimate the number of institutional pianos (schools, concert halls).
- Estimate the tuning frequency for all pianos to get total annual tunings (demand).
- Estimate the number of tunings one professional can perform per year (supply).
- Divide total demand by individual supply to find the number of tuners."
Assumptions & Calculations (Verbalized):
- "Let's start with the population of NYC, which is roughly 8 million people. Let's
assume an average household size of 2.5 people. That gives us approximately 3.2
million households."
- "Now, what percentage of households own a piano? It's not as common as it used to
be. I'll assume it's a relatively affluent or musically inclined household. Let's
estimate 1 in 40 households has a piano. So, 3.2 million divided by 40 is 80,000
household pianos."
- "Next, institutional pianos. Let's consider schools, concert venues, bars, etc. This
is harder to estimate, but let's say they add another 25% to the total. So, 80,000
times 1.25 gives us a total of 100,000 pianos in NYC."
- "For tuning frequency, let's assume residential pianos are tuned once every two
years on average, and institutional pianos are tuned twice a year due to heavier
use. This gives us (80,000 / 2) + (20,000 * 2) = 40,000 + 40,000 = 80,000 tunings
per year."
- "Now for the supply side. A full-time tuner might do 2 tunings per day, and let's
say they work 5 days a week for 50 weeks a year. That's 2 * 5 * 50 = 500 tunings
per year per tuner."
Resolve & Sanity Check: "Finally, I'll divide the total
demand by the supply per tuner: 80,000 total tunings divided by 500 tunings per tuner
gives us 160 piano tuners. This number feels plausible—it's not thousands, nor is it
just a handful. It suggests a specialized but sustainable profession in a city of this
size."
6.2 Logical & Deductive Reasoning
Question: "You have 10 jars of pills. Each pill weighs 10 grams, except for one jar of
'heavy' pills, where each pill weighs 11 grams. You have a digital scale that you can use
only once. How do you identify the heavy jar?"
Common Pitfall: Thinking about weighing each jar separately, which violates
the "one weighing" constraint. The key is to create a single measurement that encodes
information from all jars simultaneously.
Detailed Solution:
Calm & Clarify: "Okay, so I have 10 jars, one of which is
filled with pills that are 1 gram heavier than the rest. I have a digital scale, and I
can only perform a single weighing. My goal is to identify the heavy jar."
Structure & Think Aloud: "Since I only get one
measurement, I need to devise a sampling strategy where the final weight on the scale
points directly to the heavy jar. I can't just weigh a pill from one jar. I need to take
a different number of pills from each jar. This way, the amount of 'overage' in the
total weight will tell me which jar contributed the heavy pills."
Assumptions & Calculations (Verbalized):
- "First, I will label the jars from 1 to 10."
- "Then, I will take a number of pills from each jar that corresponds to its label.
So, I'll take 1 pill from jar #1, 2 pills from jar #2, 3 pills from jar #3, and so
on, up to 10 pills from jar #10."
- "This gives me a total of 1+2+3+...+10 = 55 pills."
- "Now, I need to calculate the 'baseline' weight. If all the pills were standard (10
grams), the total weight would be 55 pills * 10 grams/pill = 550 grams."
- "I will place all 55 pills on the scale for my single weighing."
Resolve & Sanity Check: "The final weight on the scale
will tell me which jar is heavy. The 'extra' weight in grams above 550 will correspond
exactly to the jar number. For example:
- If the scale reads 551 grams, the overage is 1 gram. Since I took 1 pill from jar
#1, that must be the heavy jar.
- If the scale reads 552 grams, the overage is 2 grams. Since I took 2 pills from jar
#2, and each heavy pill adds 1 gram, jar #2 must be the heavy one.
- If the scale reads 560 grams, the overage is 10 grams, pointing to jar #10.
This method works for any of the 10 jars and uses only one weighing."
6.3 Mathematical & Quantitative
Question: "You have a 3-gallon jug and a 5-gallon jug. How do you measure out exactly 4
gallons of water?"
Common Pitfall: Getting stuck in a loop of filling and emptying jugs
without a clear goal. The solution requires thinking about how to use the difference in
volumes (5 - 3 = 2) or combinations to isolate the target amount.
Detailed Solution:
Calm & Clarify: "Okay, I have a 3-gallon and a 5-gallon
jug, and my goal is to isolate exactly 4 gallons. I'll assume an unlimited supply of
water and a place to discard excess water. I'll use my pen and paper to track the volume
in each jug at each step."
Structure & Think Aloud: "I need to get to 4 gallons. I
can't do it with one jug. I need to use them in combination. I can either try to get 4
gallons in the 5-gallon jug or by combining water from both. Let me try to get 4 gallons
in the 5-gallon jug. This means I need to remove exactly 1 gallon from it when it's
full. I can do that by pouring water from the full 5-gallon jug into the 3-gallon jug
until it's full, but I need space in the 3-gallon jug. Let me try another path."
Assumptions & Calculations (Verbalized - Trial and Error):
- Step 1: Fill the 5-gallon jug completely. (State: 5G jug = 5, 3G
jug = 0)
- Step 2: Pour water from the 5-gallon jug into the 3-gallon jug
until it is full. (State: 5G jug = 2, 3G jug = 3)
- Step 3: Empty the 3-gallon jug. (State: 5G jug = 2, 3G jug = 0)
- Step 4: Pour the 2 gallons from the 5-gallon jug into the 3-gallon
jug. (State: 5G jug = 0, 3G jug = 2)
- Step 5: Fill the 5-gallon jug completely again. (State: 5G jug = 5,
3G jug = 2)
- Step 6: Carefully pour water from the 5-gallon jug into the
3-gallon jug until the 3-gallon jug is full. Since it already has 2 gallons, it will
only accept 1 more gallon. (State: 5G jug = 4, 3G jug = 3)
Resolve & Sanity Check: "At the end of this process, I
have exactly 4 gallons of water remaining in the 5-gallon jug. This solution works and
follows all the rules."
6.4 Lateral Thinking & "Out-of-the-Box"
Question: "A man is found dead in a room with no doors or windows. The only things in the
room are the man, a puddle of water, and some broken glass. How did he die?"
Common Pitfall: Focusing on conventional causes of death (murder, suicide)
and trying to explain how a person or weapon got into a sealed room. The key is to challenge
the assumption that the "man" is human.
Detailed Solution:
Calm & Clarify: "Okay, a sealed room, a dead man, water,
and broken glass. I need to explain the cause of death. The 'no doors or windows' detail
seems critical, suggesting an unconventional entry or situation."
Structure & Think Aloud: "The standard explanations seem
impossible due to the sealed room. This suggests that the premise itself contains a
trick. I should re-examine the words. 'Man,' 'room,' 'water,' 'glass.' What else could
they mean? The puddle of water and broken glass are the main clues. What object involves
a man, water, and glass, and could break?"
Assumptions & Calculations (Verbalized): "Let's challenge
the core assumption: is the 'man' a human being? What if he's not? The combination of
water and glass makes me think of a container. A fish tank or a goldfish bowl. If the
'man' was a goldfish, and the bowl fell and shattered, the goldfish would be left in a
puddle of water on the floor, where it would die."
Resolve & Sanity Check: "The 'man' was a goldfish. The
broken glass and puddle of water are from his shattered bowl. This solution explains all
the elements in the room and resolves the paradox of the sealed room. The question is a
lateral thinking puzzle that plays on the word 'man'."
Section 7: Preparation Resources for the Modern Candidate
Effective preparation for brain teaser questions is not about memorizing hundreds of answers. It is
about developing the underlying cognitive skills and strategic frameworks that allow a candidate to
tackle any novel problem with confidence. This section provides a curated list of resources to help
candidates build these core competencies.
7.1 Beyond Memorization: Building Core Problem-Solving Skills
The most durable preparation strategy is to strengthen the fundamental skills that brain teasers are
designed to measure.
- Practice with Case Studies: For roles in consulting and business, practicing
full case studies is often a more valuable use of time. Case
studies test the same analytical and structured thinking skills as brain teasers but within a
more realistic business context. They provide a better simulation of the actual work involved.
- Master Behavioral Interview Frameworks: As many top companies have replaced
brain teasers with behavioral questions, mastering frameworks like STAR (Situation, Task,
Action, Result) and SOAR (Situation, Obstacle, Action, Result) is critical. These frameworks
help structure answers to questions like "Tell me about a time you solved a complex problem,"
forcing a candidate to demonstrate their problem-solving process through real-world examples.
This is a key part of maximizing your learning experience.
- Engage in General Cognitive Training: Regularly engaging in activities that
challenge the brain, such as chess, Sudoku, or other logic puzzles, can help improve mental
agility and problem-solving speed. Platforms like Mind Hustle use gamified learning and spaced repetition to achieve this, showing how a gamified path can lead to skill development.
7.2 Recommended Books and Literature
Several books are highly regarded for preparing for quantitative and consulting interviews, often
including sections on brain teasers and logical puzzles.
- Heard on The Street: Quantitative Questions from Wall Street Job Interviews by
Timothy Crack: A classic and widely recommended resource, this book provides a large collection
of quantitative questions and brain teasers frequently asked in finance and trading interviews.
- A Practical Guide To Quantitative Finance Interviews by Xinfeng Zhou: Often
referred to as "The Green Book," this is considered an essential text for anyone preparing for
quant interviews. It covers a broad range of topics, including a significant number of brain
teasers that test probability, logic, and mathematical reasoning.
- Books by Jean Peyre: Author of several targeted interview prep books, including
Cracking the Finance Quant Interview and Brain Teaser Interview Questions,
which offer collections of recent and relevant problems with detailed solutions.
- Brain Teasers to Build Critical Thinking Skills by Kris Safarova: This book
focuses on the broader goal of enhancing critical thinking through puzzles. It categorizes brain
teasers by difficulty and provides not just answers but detailed explanations of the logic
required to solve them, making it a valuable tool for skill-building.
- How Would You Move Mt. Fuji? by William Poundstone: While some of its examples
are now dated, this book was one of the first to popularize and deconstruct the logic behind the
brain teaser questions used by companies like Microsoft and is a good source for understanding
the history and style of lateral thinking puzzles.
7.3 Top Websites and Online Forums for Practice
Online platforms and communities offer a dynamic way to practice puzzles and engage with others
preparing for similar interviews.
- Websites for Practice Puzzles: BrainBashers, Braineaser, SharpBrains, Lumosity
& MentalUP. These sites offer a variety of logic, word, and rebus puzzles designed to test and
exercise different cognitive functions.
- Online Forums and Communities:
- Reddit: Subreddits like r/quant, r/consulting, and r/engineering are
active communities where members frequently post and discuss interview questions.
- QuantNet: A highly specialized forum for students and professionals in
quantitative finance with extensive interview preparation threads.
- Glassdoor: While primarily a company review site, its interview
sections often contain user-submitted questions, giving candidates insight into the
specific types of questions being asked at target companies.
- Hacking the Case Interview:
Provides specific guides and examples for consulting-style brain teasers.