Change Management

During a consulting interview, it is likely that a potential candidate will be given a brain teaser in order to assess the individual's ability to logically work through a problem.

With this in mind, I thought I'd attempt to unearth one of the most intriguing questions of all time and perhaps the greatest brain teaser ever given to a potential consultant candidate.

Some brain teasers include: Why are manhole covers round?, How many pennies would it take to reach the top of the Empire State Building?, How many golf balls fit into a Boeing 747? (Vault.com)

As you can see, the questions are quite abstract and probably would tell an interviewer a great deal about how that applicant works through ambiguous problems. But, after a while, these same brain teasers can become boring. Therefore, I wanted to work through my very own brain teaser that I find particularly interesting.

• How much time does the average person engage in sexual intercourse during their lifetime?

In order to answer this question we have to consider many things, but it will be necessary to break down one's lifespan into sizable chunks that can be dealt with in a logical way, due to the fact that people are engaging in more or less sexual activity depending on their age on average.

First, some background information. I am only going to figure this out for the United States population. Other countries may be having more or less sexual intercourse over a lifetime. The average lifespan for an individual living in the United States is 78.06 years according to Wikipedia. This ranks as tied for 30th place in the whole world. The life expectancy is slightly different for males and females, but for purposes of this brain teaser, we will just take the average age.

Now we have to consider when people actually start having sexual intercourse. According to a publication by American Sexual Behavior, an individual's first sexual experience will occur around the age of 17 years. I will then assume that once an individual starts having sexual intercourse they will be able to continue to do so. Therefore, there are 61.06 years of life in which sexual intercourse is possible on average.

However, the frequencies of sexual intercourse are different depending on the phase of life you are in. Consider the frequency of sexual intercourse individuals will typically have when first starting to have sexual intercourse versus when someone gets married versus when someone is a lot older.

To uncover the frequencies of sexual intercourse in one's life I drew research done from the 2005 Durex Global Sex Survey. The results are based on a responses from almost 317,000 people worldwide. This is considered one of the most comprehensive sex surveys in the world.

According to the survey results, people aged 16-20 are engaging in 90 sexual experiences a year compared with 108 sexual experiences for 25-34 year olds, but the highest frequency of sexual intercourse is occurring for individuals aged 35-44 years with 112 sexual experiences a year.

Based on this data, I constructed a graph that would express the average amount of times per year an individual was having sexual intercourse at each age between 0 and 78.

Looking at the graph, I want to explain a couple features. First, the solid blue line is based on factual data that was attained and the black line is a polynomial function that best fits the data provided. The blue line is at 0 until age 17, because this is the first time that people engage in sexual intercourse on average according to documented research. Then, I graph the levels attained by Durex's Sex Survey for ages 16-20, 25-34, and 35-44. According to Durex, 35-44 year olds are having the "most" sex. Therefore, I consider the amount of 112 sexual intercourse experiences a year as my maximum and projected the data after the age of 44.

In order to make these projections, I found out that "Among 60- to 70-year-olds with partners, 46 percent of men and 38 percent of women have sex at least once a week" (HealthyMe). Therefore, I assume that at age 65 individuals are having 50 sexual experiences a week on average, which is a decline of 2.95 sexual experiences per year from 45 years old to 65 years old.

I then assume that at age 78 there are no longer any opportunities for sexual intercourse, on average, and therefore find the rate of decline from 50 sexual experiences at age 65 to 0 sexual experiences at age 78. This is a decline of 3.85 sexual experiences per year, on average.

Using the Trendline tool in Excel, I fit the graph that I had constructed with a binomial function that could generally explain for the amount of sexual intercourse an individual has per year, on average, based on the research I had collected.

The binomial function is equal to:

Where x is equal to the age of the individual. Using this formula, I was able to figure out the amount of times per year an individual has sexual intercourse from age 17 through 78, on average, for each year.

In order to figure out how many times during a lifetime an individual will likely have sexual intercourse, I find the sum of the frequency of sexual intercourse episodes a year for each year from 17 through 78. This is expressed as:

Performing this calculation, I arrive at a total of 4835.05 instances of sexual intercourse over the average lifetime for the average individual in the United States.

But, I am not done yet. I now need to find out how much time this equals. According to the Durex Global Sex Survey, "Americans spend 35 minutes on foreplay and sexual intercourse each session" (Source).

Therefore, by simply multiplying 4835.05 by 35 minutes, I arrive at the total amount of time having sexual intercourse in minutes for the average American. The amount of time spent having sexual intercourse over the average lifetime is therefore: 169,226.8 minutes.

This value is equal to 2820.4 hours and 117.5 days. In terms of an individual's average lifetime, the amount of time having sexual intercourse only equates to 0.41% of total life activities, on average.

• Conclusion

In order to figure out the amount of time an individual has sexual intercourse over a lifetime in the United States on average, I found out when people start having sexual intercourse and what the average life expectancy is. This gives an average "window of opportunity" for sexual intercourse.

Then by researching the frequencies of sexual episodes per year for various age segments of the population, I was able to determine a binomial function that expresses the amount of sexual experiences had for each year during the "window of opportunity."

I then added these to arrive at the average amount of sexual intercourse experiences had in a lifetime. I found that it was approximately 4835 sexual intercourse experiences in an average American lifetime.

I then found out the average length of time a sexual intercourse experience lasts, 35 minutes, and multiplied this number by the amount of sexual intercourse experiences over an average lifetime.

This calculation gives us our answer to the brain teaser, "How much time does the average person engage in sexual intercourse during their lifetime?" The determined value is 169,226.8 minutes or 2820.4 hours or 117.5 days or 0.41% of the average person in the United States' life.

Louvre Thought Exercise

At the moment I find myself in Paris as my journey across Europe comes to a close. Paris is one of the biggest, most exciting, and beautiful cities I have ever had the chance to be in. It is truly spectacular how it is capable of maintaining its beauty, but at the same time, pump like big cities do. In some ways it reminds me of New York, just far more beautiful, historic, and everything happens to be in French.

Anyway, while I've been here I've had the opportunity to visit some of the most amazing museums in the entire world. I have seen the Museum D'Orsay which houses a humongous collection of Monet, Manet, Van Gogh, Whistler, Degas, and Renior. I loved this museum very much and if you're in Paris you cannot miss it. And of course, if you're in Paris and you're checking out some museums, it is an absolute must to go and visit the most famous and most visited museum in the entire world, the Musée du Louvre.

The Louvre houses the most famous piece of art in all the world, The Mona Lisa by Leonardo Da Vinci. It also has the famous, Venus de Milo, which is supposedly a sculpture of the Greek Goddess Aphrodite that was found in 1820 by a peasant on the Aegean islands of Milos. Beyond these two astronomically famous works of art, there is just hoards and hoards of art that fill this museum. It would probably take three very long lifetimes to be able to really see all the Louvre has to offer.

Although I was absolutely blown away and impressed with the artwork and sculptures in the Louvre, I was equally impressed with the actual structure of the museum. The inside was as beautiful as any palace I have ever seen, and its immense size is almost unfathomable. I spent a good three hours there and don't think I left the single wing I entered into. It is truly enormous. At the same time though, it is so beautiful and ornate.

This got me thinking what all of this must have cost the French Government. I learned a lot about the process of making the Louvre and how it arrived at its present state, and wanted to figure out how long it will take for the Louvre to break even (if ever).

• Louvre Thought Exercise

According to the 9th Edition of Frommer's Europe Guidebook, the Louvre recently undertook a renovation known as The Grand Louvre Project that cost an astronomical $1.2 Billion and took 15 years to complete. The book goes on to further cite that there are individual galleries that are constantly being renovated, but that is to be expected. So, to clarify, in this thought experiment, our total cost of the Louvre is $1.2 Billion (the other galleries can be considered in another though experiment at some other time perhaps).

That's a pretty good chunk of change to use on a building. I wanted to learn further about The Grand Louvre Project, because perhaps that would give me insight as to how it was going to be paid for or when they expected to make a profit on the Museum.

According to the Harvard Design School Center for Design Informatics Executive Summary on the Grand Louvre, The Grand Louvre Project was just one of several renovations and projects that were proposed by prior French president François Mitterrand. Other projects that were underway during his presidency were the new Bibliothèque Nationale de France, the Opéra des
Bastille, and the Grande Arche de la Défense (collectively known as the “Grands Travaux” or Grand Projects). I have personally had the opportunity to see the National Library and Grande Arche, in addition to the Louvre, and they are spectacular sites to see in Paris as well.

The operation to renovate and construct new additions to the Louvre began in 1981 in which the design phase first started. The chief architect chosen to direct the project was I. M. Pei (the glass pyramid that serves as the entrance to the Louvre is named for him today).

The project was split into two phases. The first phase was renovation of 61,990 square meters. This part of the project also included demolishing 55,000 square meters. Phase two was the addition of 50,000 square meters of usable gallery space. Between 1981 and 1998 these two phases were realized. What a serious undertaking.

Now that we have a thorough understanding of the project, let's see if the money I spent to get in the door this past Friday went to the Louvre or into the pockets of the Director and Curator of the Museum.

• Vital Information

1. It cost 9 Euro to enter the museum
2. It costs 6 Euro to enter the museum between 6pm and 10pm on Wednesdays and Fridays
3. The Museum is open 6 days a week, and is closed on January 1st, May 1st, November 11 and December 25, 2008
4. The hours of operation are from 9am to 6pm regularly
5. The first Sunday of every month is free for visitors
6. Children 17 and under are free
7. Guided tours are 6 Euro a person, but free for children under 12
8. Audioguides are 5 Euro

Okay, here we go:

According to an article published by Bloomberg.com, the Louvre is the world's number one visited museum in the world with 8.3 million visitors annually. First, I want to break down these 8.3 million people by age.

**Click the Image to see it more clearly**
By looking at figures provided by the US Census Bureau for the World Population, I can extrapolate roughly what the demographics of these 8.3 million people would be. Obviously it cannot be perfectly accurate, because you would have to take into account an individual's preference to view art, whether or not they had enough time while in Paris, etc. However, this will give us a very good representation of how these 8.3 million people are composed. These numbers are also represented graphically in the following chart.

So now that we have a sufficient break down of the people entering the Louvre we can figure out who is next paying for what. We will figure this out on a yearly basis, and then we will move forward from the year 1998 to the present to see when or if they have broken even regarding the initial $1.2 Billion investment.

Now, let us find out how many days the Louvre is open. If there are 52 weeks in a year and the Louvre is open 6 days a week, then that totals 312 days. However, it isn't open for four of those days, so that now means it is only open for 308 days out of the year. We're doing great.

**Click the Image to see it more clearly**

Now, if we assume that the same amount of people enter into the Louvre each day on average, we arrive at the conclusion that there is 8.3 million people over 308 days this equals, 26,948 visitors per day that the Louvre is open. Obviously some days will be busier than others, but this is purely on average.

For simplicity sake it will be better to find the average length of a day.

If we know that 4 out of 6 days are going to have 9 hours, and 2 out of 6 days are going to have 13 hours we simply perform the following equation: 4/6(9 hours) + 2/6(13 hours) = 10.333 hours.

Therefore, on a given day at the Louvre, it will be open for 10.333 hours or 10 hours and 20 minutes on average. It is also important to find out the average payment made by a person entering the Louvre, due to the fact that in addition to hours of operation changing, price also changes.

It will be best if we do this average on an hourly scale. In a week, there are five full days in which full price is paid, Monday, Wednesday, Thursday, Friday, Saturday. This equates to 45 hours of full payment. On Wednesday and Friday, there are an additional 4 hours each in which the price of entry is reduced. Sunday is a little more complicated.

Remember, the first Sunday of every month is free, so 12 out of 52 Sundays in a year are free, but the others are not. Tuesday is not considered because the Louvre is closed then.

So, we arrive at the following equation for average price paid: (45(9 Euro) + 8(6 Euro) + (40/52)(9 hours)(9 Euro))/59.92 hours = 8.60 Euro. The 59.92 hours is the average length of time the Louvre is open a week, not including the holiday closings. It is divided out to give an average hourly entrance rate.

We can also find out how many people enter the Louvre per hour. By taking 26,948 and dividing it by 10.333 hours, we arrive at an hourly rate of 2,608 people per hour.

Next we need to figure out how many people are aged under 12 and under 17 years of age, due to fees associated with entrance and tours. To do this, we will assume that there is an equal number of people in each age year within each age category. Therefore, there are the same amount of people within the age category 0-19 who are 2 years old as there are 18 year olds.

If we know that there are 2,996,383 people in the 0-19 category, all we do is divide this category by 20 to get an equal rate of people for each year. Therefore, there are 149,819 people in each year. To figure out how many are 12 and under, we multiply this number by 13 (remembering that 0 is included in the count), and the same is done for 17, except this number is then multiplied by 18.

This gives us 1,947,648 people 12 years and under, or 6,324 per day and 2,696,745 people 17 years and under, or 8,755 per day.

• Recap
• Louvre is open 308 Days a year
• 26,948 people visit per day
• An average day's length is 10.333 hours or 10 hours and 20 minutes
• On average, it cost 8.60 Euro to enter the Louvre
  
• 2,608 people visit per hour
• There are 6,324 people 12 years and under per day
• There are 8,755 people 17 years and under per day
  

Now we can start figuring information out. Based on the information we have compiled, it would be best to figure out our estimates on a daily basis.

• Money made on entrance fee to the Louvre per day: (26,948-8,755) x 8.60 = 156,459.80 Euro
• Assuming 35% of people go on guided tours, Money made on guided tours at the Louvre per day: 0.35(26,948-6,324) x 6 = 43,310.40 Euro
• Assuming 35% of people use Audioguides, Money made on Audioguides at the Louvre per day: 0.35(26,948) x 5 = 47,159 Euro
  

Therefore, the Louvre makes 156,459.80 + 43,310.40 + 47,159 = 246,929.20 Euro per day.

Over a year of open days numbering 308, the Louvre will expect to make: 308(246,929.20 Euro) = 76,054,193.60 Euro per year.

There have been 10.5 years since completion of the Grand Louvre Project in 1998. Therefore, based on this information the Louvre has brought in: 10.5(76,054,193.60 Euro) = 798,569,032.80 Euro.

Recall that the amount it took to perform the project was in Dollars. Therefore, all of my figures that are in Euros need to be converted to Dollars. 1 Euro will buy you 1.5756 Dollars as of June 8th, 2008.

With this in mind, I constructed a chart that would show when the Louvre would "break even." According to my findings, the Louvre would have surpassed the $1.2 Billion initial expense at the beginning of 2007.

**Click the Image to see it more clearly**

• Conclusion

The Grand Louvre Project was a huge undertaking for the city of Paris. It was a 17 year endeavor that cost over $1.2 Billion. Since the projects completion in 1998, the Louvre has brought in 76,054,193.60 Euro ($119,830,987.40) per year, based on our gathered information. This means that the Louvre covered its initial operating expense early in the year 2007.

The Louvre is an incredible project and well worth the money and time that was put into it. Walking through it was an incredible experience. If you make your way to Paris, this is one stop you're most definitely going to want to make.

McKinsey Preview Weekend

I was recently directed to a potential opportunity this summer with mega-consulting firm, McKinsey & Company. They are running this Mckinsey Preview Weekend in Washington, DC from July 25th to the 27th. According to the web page:

McKinsey Preview Weekend (MPW) is designed to provide rising juniors and seniors with an early introduction to management consulting in general, and McKinsey & Company in particular.

This participatory weekend workshop will include:

• Group discussions led by current consultants to help you explore the consulting industry
• Team activities designed to help you experience first hand the type of work we do at McKinsey
• Opportunities to connect with McKinsey consultants and fellow student participants

Preview Weekend is open to rising college juniors and seniors.

candidate criteria for MPW

• Rising juniors and seniors, from all majors, who are beginning to explore their career options
• A demonstrated ability to successfully balance academics with other responsibilities, including leadership roles and work experience
• Enjoy working on teams and solving problems

Application Details

The on-line application will take 10-15 minutes to complete. To apply, you will need the following:

• Resume
• Transcript (unofficial is acceptable)
• Essay (see topic below)

I figured that there would be no harm in at least applying to it. I must admit though, even though I am a fine student, McKinsey truly only admits the best into their company, and I feel like my chances of getting this are slim. But, if you don't ask, you don't get. So, I figure the worst thing that could happen is I don't get it, and then, I'm no worse off than I ever was.

Another reason I really wanted to apply for this, aside from the fact that it would be an amazing learning experience and awesome way to get to know new people and the company itself, was I really liked the essay question that they wanted the applicants to answer. Here is the essay question along with my answer.

• It has been said that one quality leaders possess is vision. In your opinion, what are other qualities that great leaders possess? (500 words or less)

In the film, Any Given Sunday, Al Pacino plays Tony D’Amato, the leader and coach of modern day gladiators who battle in their own Colosseum, the football arena. Prior to a pivotal game, Al Pacino stands before his warriors and proclaims, “life is just a game of inches/the margin for error is so small/ One half second too slow or too fast and you don't quite catch it.” These fateful words point to one of the most essential qualities that great leaders must possess and that is the ability to execute.

Whether you’re the leader of a school group project or a Fortune 500 company, an effective leader must have the ability to demand and produce results. People can sit around and talk all day, but if nothing is ever accomplished, then all is lost.

The ability to execute is a quality directly tied to a leader's effectiveness. It is critical to have an unbelievably strong sense of self if you are planning on leading others to success. If you don’t have a clear understanding of yourself, then how can you expect others to understand who you are? Self-awareness is a state of being that leaders should want and work to master.

Leaders must also craft a culture of execution. Those visions and goals that leaders inherently possess should be translated into tangible deliverables and actions to streamline and guide the team to achieve. Every action should have a purpose. Every team member should wake up motivated to accomplish the same ends as his counterparts.

Being able to effectively execute also means having the capacity to place the right people in the right places. Having a thorough understanding of how to delegate tasks can make or break any undertaking. A team is only as strong as its weakest link, and leaders should have the foresight to provide coaching or training if necessary.

If a leader has any hope of producing results, he or she must also have an unwavering commitment to assessing reality. Leaders cannot be thrown or distracted by smoke and mirrors. Leaders must be able to dig through a swarm of absurdity, maintain poise, and remain firmly on track to realizing the goal. Superb leaders do not have time to get lost with the rest of the crowd.

Without doubt, the art of execution separates the few from the many. Microsoft CEO, Steve Ballmer, also thinks that execution is an essential part of leadership. According to Ballmer, “I like to tell people that all of our products and business will go through three phases. There's vision, patience, and execution.”