Last night, I took my kids out for an American children’s holiday known as Halloween.
Kids (and some ahem… adults) dress up in costume (I was a penguin this year), go door-to-door, saying “Trick or Treat” and get free candy from the neighbors.
My three kids brought back a record 420 pieces of candy. 
In today’s New York Times, I learned that in the weeks leading up to this holiday, Americans purchased $2.7 BILLION dollars in candy.
So here’s my challenge for you.
Assuming all of that candy is consumed by someone in America, estimate the total number of calories represented by $2.7 billion in candy.
Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain. Add a comment below to post your entry.
The winner will receive public acknowledgement of their estimation skills, and I will send them a portion of the candy “tax” I collected from my kids.
Yes, we tax our kids for a portion of their candy collection, as mom and dad provide “infrastructure” and “chaperone” services.
It’s a useful lesson in taxation.
(We tax at a 33% tax rate.)
Mostly it is an excuse to reduce the amount of sugar they will otherwise end up consuming.
For my kids, it’s an excuse to get rid of the candy they don’t like anyways.
Good luck and Happy Halloween!
Entries will be accepted for next 72 hours, and only entries posted as comments below will be considered. A winner will be announced next week.
UPDATE as of Friday, November 4TH AT 12PM ET: New entries are welcome, but not eligible to win, as contest has closed.
329 thoughts on “A Sweet Estimation Question”
Assumptions
1. Premium candy and regular candy own 30% and 70% of the market respectively
2. Premium and Regular candy are30 and 50calories per piece respectively
3. There are no further segments that account for the variability in calories per piece of candy
4. Premium and Regular candy are $0.60 and $0.10 respectively
5. All candy sold was consumed
Candy segments
1. Premium | 30% of Market | $0.60/piece | 30 calories/piece
2. Regular | 70% of Market | $0.10/piece | 50 calories/piece
Premium Segment:
Market Share – $2.7B x 30% = $810K
Pieces Sold – $810K / $0.60 = $1.35B
Calories Consumed – $1.35B x 30 = $41B
Pounds gained 41B / 3.5K = 12M
Regular Segment:
Market share – $2.7B x 70% = $1.9B
Pieces Sold – $1.9B / $0.10 = $19B
Calories Consume – 19B x 50 = 950B
Pounds gained – 950B / 3.5K = 271M
Total Pounds gained = 283M
Ex management consultant here. Most of these answers are below par. A lot of responses are parsing out the wrong variables. Think about how you would segment different types of pricing categories for candy.
Also, the ones who are doing excessive calculations (like using exponents) ought to know that that level of detail will hurt your rating in an interview.
Facts:
– Total Spend 2.7B
– 3,500 cal = Gain of 1 pound
Liberties taken
– Round $2.7B to $3B
Segmetnt Cx Market
– Large candy bag buyers (LCB) = 25% | $750M
– Medium candy bag buyers (MCB) = 50% | $1.5B
– Small candy bag buyers (SCB) = 25% | $750M
Segment Cost per Candy bag by size
– Large = $20
– Medium = $15
– Small = $10
Segment Candy bags sold
– Large = 150M
– Medium = 225M
– Small = 75M
Segment Calories per Candy bag
– Large = 8K
– Medium = 6K
– Small = 4K
Segment Total Calories per Candy bag
– Large = 1.2B
– Medium = 1.3B
– Small = 300M
Total Calories from all Candy bags
– 2.8B
Liberties taken
– Round 2.8B to 3B
Divide Total Candy bag Calories by 3.5K
– 3B/3.5K = ~800K lbs
Total Pounds Gained
– ~800K lbs
There are two questions being asked
1.) Estimate the total number of calories represented by $2.7 billion in candy
2.) Estimate how many pounds (or kilograms) of weight American population would gain assuming 3,500 calories consumed results in a person gaining 1Ib (0.45 kg)
In order to provide a solution to the first question, we will need two pieces of information
1.) Average cost per candy, which will be assumed to be 50cents
2.) Amount of calories per candy which will be assumed to be 250 calories (calories in a 58g bar of Mars)
Given this information, the amount of candy, which can be purchased by $2.7 billion, can be calculated by dividing $2.7 billion by $0.5, which results to 5.4billion candies.
Given a portion of candy contains 250 calories; 5.4 billion candies will contain 5.4 billion multiplied by 250 calories which result to 1,350 billion calories.
Moving on to the second question asked – Estimate how many pound (or kilograms) of weight American population would gain assuming 3,500 calories consumed results in a person gaining 1Ib.
Total increase is 1,350 billion calories divided by 3,500 calories per 1Ib. This results in an increase in weight by 386 million Ib.
This is a very very “Tricky” question — one must think about “how much” candy is consumed by the different segments of the human population and how the consumption of candy individually affects each segement in terms of weight gain, because… while I seem to always gain weight after a buffet dinner, my brother seems to keep his slender figure even though he eats just about twice as much food as me…yes, it’s called the difference of metabolisim…but here are some addtional questions to consider if you are just now stumbling on this email as I have:
1.) Have you considered a reduction of human weight gain, due to the consumption of candy by the family dog, the-self-imposed-neighbor-named-house-mouse, the curious cat, or the munchy army of ants that successfully found passage through the faulty wrapper? Yes, we must also consider the element of Q.ASSURANCE for the packaged food. We can call this point weight loss reduction due to “non-human species”…but I call my dog Winston a human, so again…a very tricky question.
2.) What about the tossed out candies in the trash that didn’t fit the taste buds of our fellow Americans, or the melted candies by the sun (I’m in California so this happens, but another logical explanation is that the candies, we can presume mostly the chocolates, wanted to also dress up for Halloween as the Melted Wicked Witch, or maybe they wanted to look like a steaming pile of……) let’s move to the next point.
3.) Have we considered how many parents subjected their children, as well as the guilty consciouses of adults, to the 33% tax rate which reduced the weight gain of America? Also, remember, some tax rates are different, such as Sweeden’s which is approximately 57% and so we must also consider different influences of “national identity” that we Americans are allowed to embrace.
4.) And what about the bowl left outside of the lazy home or apartment owner, who didn’t want to greet kids but was kind enough to leave one bowl of candies with a sweet note underneath the candies that says “Sorry! We don’t have anymore candy — Happy Halloween!”
Surely, each kid didn’t just take one, a few kids stockpiled on the riches, and are still eating the candy today! Ah-Ha! We must take into consideration the segment of the population known as “stockpiler kiddos”
5.) In the advent of 9 states placing the legalizing of recreational M.J. on today’s ballot, how many people decided to forgo walking with their kids to attain “420” pieces of candy and decided to immediately tax 80% of their kids candies….only to eventually throw it back into the toilet because of overeating and too many “bowls”…this is actually 3X tricky because some can do the Dance with MJ and stretch their stomachs. I’ll leave it to you to do the math here (I’m already disqualified because my GF gave me the tip about the Sun melting candies)
6.) Last tip and question for now: we must also investigate how a Sugar high will induce a child or adult to engage in physical activity. Not only does your brain burn a good amount of calories to “think” but your body subconsciously burns calories for regulatory bodily activities, for the circulatory and respiratory processes, etc. SO! Don’t forget to estimate how much candy calories were burned off because some kids and adults were lucky to not forgo 33% of their treasure trove of candy and decided to run a half or full marathon in their homes and backyard.
END OF AREAS TO CONSIDER.
Parting Remarks: If anyone Dares to solve Mr. Penguin’s challenge with the listed elements above…I will personally drive to Victor’s office to seek a personal recommendation letter from Victor for your career path in whatever field it may be.
May the Force be with You!
* I know Victor stated: “Assuming all of that candy is consumed by someone in America” ; however, this is the ultimate consulting test — you must disagree with Victor’s assumption to prove that this assumption is too faulty to produce an accurate estimation. Consultants in interviews sometimes want to see if you will disagree (Respectfully of course) to see if you can identify faulty logic in a polite manner. Take it from the guy who messed up in this area during a consulting interview with a boutique firm in Boston.