Case

Brain Teasers - Coins

Solved 1.3k times
4.5 5 241
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Problem Definition

Coins

Situation:
Imagine, we are sitting together at a perfectly round table. We both have an infinite pile of quarters. These are the rules of the game: “We'll take turns putting one quarter down on the table, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses."

Question:
Who should start in order to win, why and how does your strategy work?

Marbles

Situation:

There are 8 marbles that weigh 1 ounce each, and 1 marble that weighs 1.1 ounces. The marbles are all uniform in size, appearance, and shape. You have a balance that contains 2 trays. You are only able to use the scale 2 times.

Question:

How do you determine which marble is the heaviest using only the scale and marbles in 2 weighings.


Comments

Brain Teasers are short questions with difficult logical or creative answers. They are a good way to test your analytical skills and capacity to think out of the box. These short questions also show the interviewer your ability to elaborate on difficult tasks from the real world. Each Brain Teaser is supposed to be solved by the interviewee in about 5-10 minutes.

If the interviewee gets stuck in a brain teaser (i.e. spends more than 10 minutes), propose to go on to the next one.

Detailed Solution

Coins

You have to start. You place a quarter exactly in the center of the table. After that, whenever I put quarter on the table, mimic my placement on the opposite side of the table. If I have a place to place a quarter, so will you. I will run out of places to put a quarter before you do.

Marbles

Place 3 marbles on each tray.

  • If the first weighing doesn't balance, remove all the marbles from the lighter side, and place one marble on each tray from the heavier tray. The heavier side is the 1.1 ounce marble, but if they balance, then the marble from the heavier tray from the first weighing that was not weighed in the second weighing is the heavier one.
  • If the marbles balance on the first weighing, remove the marbles from the trays, and place 2 of the remaining not weighted marbles on the trays, one on each tray. If one is heavier, it is the heavier marble, but if they balance, the remaining not weighted marble is the heavier one.
Related consulting question(s)
Best answer so far:
Ex BCG | MBB Specialist | #1 Expert for coaching sessions (1400+) with 100% recommendation rate

Hi Anonymous, there may be several reasons for that; some of them, in order of frequency, are: Your structure is not complete enough – you are just using not MECE/ not complete structure... (more)

Hey, I am new to this too, but I think I have some ideas for your problem. Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train e... (more)

Best answer so far:
McKinsey Engagement Manager & BCG Consultant | Interviewer at McK & BCG for 7 years | Coached 35+ candidates secure MBB offers

Hi Anonymous, first of all - this is not a brain teaaser, but an ordinary estimation question! Here is a high-level approach: I would start with the second question, because it is most straight forw... (more)

Best answer so far out of 3 answers:
Sibren
Expert
Two years conulting experience, went through lots of interviews and coached several candidates to MBB offers

Hi, good question! Probably somewhat depending on your interviewer, but this is my view on it. In this situation it's important to try to showcase as mluch of your consulting skills as possible. Be... (more)

Best answer so far out of 2 answers:
Marco
Expert
Specific coaching: company you are applying for; 1st or 2nd round; your professional background; ...

Hi, here's how I would approach it - Define the geographic area to be covered [the whole world? the U.S.? NYC? Manhattan?...for this example I'll use Manhattan] - Population living there [~ 1... (more)

Related BootCamp article(s)

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

4 Comment(s)

Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

2 Comment(s)
4.5 (241 ratings)
4.5 5 241
Case exhibits

No case exhibits yet