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”
I was going to do an delphi approach and see what the average of the expert posts look like but it seems the answers so far are all over the place, with some in the multiple trillion lbs to a few hundred thousand lb…
So taking another approach, we assume variable k to be the calorie/dollar conversion of candy:
lb gain of American population = $2,700,000,000*k/3500 cal per lb
=771,429k
so it’s just a matter of estimating k:
-small snickers may be $2 and 500 calories or so, i.e. k~250 cal,
-m &m 9oz about $3 and 1500 cal or k~500 cal/$
-reese’s peanut cup 36 pack about $22 and 230×36 cal or k~ 390 cal/$
Candy is mostly sugar so checking sugar <$1 per kg at ~3800 cal per kg. So we can be pretty certain a final retail product in small packaging size like kids candy would be several hundred to lower thousand cal/$.
Assuming then average of 500 cal/$, lb gain is ~390 million lb, so the actual range can be hundred million lb to billion lb range depending on how much candy bought at full price retail or by bulk (like at Costco's).
Assume 70% of the 2.7 billion is spent on CHOCOLATE CANDY, the remaining 30% is spent on NON-CHOCOLATE CANDY.
CHOCOLATE CANDY (CC):
$2,700,000,000 x 0.7 = $189,000,000
On average, a $10 bag of CC weighs 1000 grams
$189,000,000/$10 = 18,900,000 BAGS of CC
18,900,000 x 1000 = 189,000,000,00 GRAMS of CC
On average, 1 gram of CC contains 5 calories
189,000,000,00 x 5 = 945,000,000,00 calories of CC
NON-CHOCOLATE CANDY (NCC):
$2,700,000,000 x 0.3 = $81,000,000
On average, a $10 bag of NCC weighs 1500 grams
$81,000,000/$10 = 8,100,000 BAGS of NCC
8,100,000 x 1500 = 12,150,000,000 GRAMS of NCC
On average, 1 gram of NCC contains 3.5 calories
12,150,000,000 x 3.5 = 42,525,000,000 calories of NCC
ADD the calories of CC and NCC together:
945,000,000,00 42,525,000,000 = 137,025,000,000 CALORIES represented by 2.7 billion in candy sales (!)
Victor says: 3,500 calories leads to 0.45 kg weight gain…
137,025,000,000 / 3,500 = 39,150,000
39,150,000 x 0.45 = 17,617,500 kg of WEIGHT GAIN
[Assume there are 320 million people in the US. On average, each person would gain 17,617,500 / 320,000,000 = 0.055 kg]
Assumptions:
US$ 2.7 billion in candy
Average price per piece:
US$ 0.20
Total pieces:
13.5 billion
Average number of pieces collected per “child in costume”:
80 (the record is 420 between 3 kids & a penguin)
Number of trick-or-treaters (assuming all candy was distributed):
168,750,000
Average Calories per piece:
50
Total Gross Calories:
675 billion
Average distance walked:
1 mile
Average calories consumed by walking:
50
Total Calories Burnt from trick-or-treating:
8.4 billion
Total net calories:
666.6 billion
Total net weight increase in pounds:
190.446.429
Average weight increase per “trick-or-treater”:
1,13lbs
Hi Victor,
From the phrasing of your question I understand that the task at hand is to estimate the total weight gained in kilos (I’m European) by the American population after consuming $2.7 billion worth of candy in the weeks leading up to Halloween.
I know from the information you provided that a person (I assume this is an average candy eater) consuming 3,500 calories of candy gains 0.45 kg in weight. I also know that all of the $2.7 billion worth of candy will be consumed by Americans.
So, given the task at hand and the information provided I know there are two major unknowns I need to estimate.
The first unknown would be how much candy does actually $2.7 billion buy (in kilos), and the second unknown is how many calories this amount corresponds to.
I think that the first unknown is more difficult, so I will start off with that. After that I will continue with the estimation of unknown nr two, and finally I will add up the results from the two estimations and come up with the final answer.
Unknown nr one; the weight in kilos of $2.7 worth of candy bought by Americans in the weeks prior to Halloween:
Before we dig deeper it is important to consider the type of candy that is bought, as I would hypothesize there is a price and weight difference between different types of candy. To illustrate, a branded candy bar probably weighs less but cost more per kg than unbranded and cheaper pieces of candy. For this reason, I will break candy down into two buckets.
I will say that 40% of candy consumed in the US ahead of Halloween (sales value) is (A) branded candy bars and 60% is (B) cheaper candy that is eaten in larger quantities.
I base this assumption on my general perception of the US, and from what I’ve seen from being there and from what I’ve heard and seen in movies. Also, I think that the proportion of cheaper candy to branded candy bars is higher prior to Halloween than at other times during the year as a lot of the candy will be given away to people doing “trick or treat” etc.
I could do a further segmentation here where I segment types of candy further, and I could also divide this into buckets of the population (i.e. adults would generally eat less candy but more expensive candy). However, I don’t think the effort is worth the reward in this instance, and I think my estimate will be accurate enough using my methodology.
From my assumption I know that approximately $1.1 billion of the $2.7 billion is branded candy bars (40% of 2.7 = 1.08) and approximately $1.6 billion is cheaper candy eaten in larger quantities (60% of 2.7 = 1.62)
(A) Estimating the weight of the branded candy bars:
From myself being in the US major cities (like NY, Chicago and Washington), I think that a branded candy bar is about $1,5. However, I do think this is more than the price in smaller cities (i.e. a couple of hundred thousand and less) or in the country side, where I would guess the corresponding price would be about $1.
I also think that people in smaller cities and the country side eat more than people in larger cities (given health trends etc.), so lets assume that 40% of the candy bars are consumed in major cities at $1,5 per piece and 60% of the candy bars are consumed in smaller cities and in the countryside at $1 per piece. Lets also assume that a candy bar weighs about 50grams.
The calculation that follows looks like this (remember the $1.1 billion worth of branded candy bars from above):
Branded candy bars in major cities:
40% of $1.1 equals approximately $0.44 billion, or 440 million. I know that a bar in the cities cost $1,5 per piece, which gives me approximately 290 million bars consumed in US major cities ahead of Halloween (440/1.5=293).
Branded candy bars in smaller cities and countryside:
60% of $1.1 equals approximately $0.66 billion, or $660 million. I know that one bar cost $1 per piece, which gives me another 660 million candy bars sold in smaller cities and the countryside in the weeks prior to Halloween.
Adding the figures up, this gives me a total of 950 million bars of branded candy bars consumed by Americans in the weeks leading up to Halloween. As a sanity check, this would be just over 3 bars per individual in the US (population of approximately 300 million), and I think this seems reasonable. To clarify, I am familiar with the shortfalls of this sanity check, e.g. babies don’t eat Snickers, some people eat zero whereas others eat multiple etc., but I think it serves the purpose of putting things in perspective. Should the estimate have given me 100 bars per individual, I would know I was completely off.
Given that a bar weighs around 50g, and 50g is equal to 0.05kg, I know that the 950 million candy bars weigh approximately 50 million kg (950*0.05 = 47,5).
It should also be pointed out that I don’t absolutely need to calculate the weight of the bars at this stage (as I in this particular instance will estimate calories per candy bar and not per 100g of candy bars). However, I chose to do so as it will give me a figure to put in perspective with the weight of the cheaper candy.
(B) Estimating the weight of cheaper candy sold in larger quantities:
Being from Sweden I am not used to buying this type of candy in the states, so I might be a little bit off in this estimate. However, I would think that this type of candy is cheaper in Americas than in Sweden, mostly due to a higher VAT in Sweden. Also, based on personal experience I would say prices are generally lower in the US, especially on sweets and candy (given current FX-rate). So, in this instance I am going to assume that prices for this type of candy in the US is about 30% cheaper in the US than in Sweden. I also know that the FX-rate SEK/USD is around 0.11.
I know that from being in a grocery store in Sweden you can buy candy per kilo. When buying candy per kilo I would say that SEK 100 would buy about 1.5 kilos worth of candy. As SEK 100 given a FX-rate SEK/USD of 0.11 would equal approximately $11 (100*0.11) this would buy 1.5 kilos worth of cheap candy in Sweden.
As prices are 30% lower in US, I know that $11*(1-30%) equals approximately $8 which will give me 1.5kg of cheap candy in the US. For ease of calculation, I put the value in whole kilos instead, i.e. $5 gives me 1kg of cheap candy ($8/1.5 = 5.3).
I also know from before that the sales value of the cheaper candy in the US ahead of Halloween equals $1.6 billion (the remaining 60% of the total $2.7 billion). As $5 gives me 1kg candy, I know that the $1.6 equals approximately 320 million kilos of candy ($1.6 billion/$5).
In total, my estimate for the first unknown gives me that Americans consume approximately 370 million kilos of candy ahead of Halloween (50 million kilos of branded candy bars plus 320 million kilos of cheaper candy).
To put this in perspective, this equals about 1.2 kilos of candy consumed per person (again, population of approximately 300 million) in the weeks prior to Halloween, which I think sounds reasonable. Thus, I would say that my estimate is on track this far.
Another sanity check is the fact that the candy bars account for approximately 15% of the total weight of the candy (50 million kg/370 million kg) but account for 40% of the consumption (sales value). This would be in line with my previously stated hypothesis, i.e. that a branded candy bar cost more but weigh less than the cheaper candy.
Unknown nr two; the number of calories per unit of weight:
In this estimation, I will come up with the average amount of calories per 100 grams of candy for the different types of candy.
Calories for (A) branded candy bars:
I would assume that one candy bar that weighs 50g would contain between 200-300 calories. Lets go forward with the assumption that one bar of 50g contains 250 calories. From this, I know that 100g of branded candy bars contains 500 calories, and I further know that 1kg of branded candy bars contains 5,000 calories.
Calories for (B) cheaper candy:
I would assume that this type of candy contains fewer calories per gram than the branded candy bars. I will move forward with the assumption that 100g of cheap candy contains 300 calories, which would be about 60% of the calories per 100g of a candy bar. I think this is reasonable. This gives me that 1kg cheap candy contains 3,000 calories.
Summary of estimation:
In this part, I will just add all the figures together. I will first calculate the calories consumed per type of candy. Second, I will summarize the results to the total number of calories consumed ahead of Halloween. Third, I will calculate the corresponding weight gained by the American population.
Summary for (A) branded candy bars:
I know from my estimation of unknown nr one that a total of 50 million kilos of candy bars are consumed by Americans per year, and I know from my estimation of unknown nr two that one kilo contains 5,000 calories. Multiplying these two figures would give me the nr of calories consumed from branded candy bars, and the answer is 250 billion calories (50 million*5,000=250 billion).
Summary for (B) cheaper candy:
I know from my estimation of unknown nr one that a total of 320 million kilos of cheaper candy is consumed by Americans per year, and I know from my estimation of unknown nr two that one kilo contains 3,000 calories. Multiplying these two figures together would give me the nr of calories consumed from cheaper candy, and the answer is 960 billion calories (320 million * 3,000 = 960 billion).
When adding the two calculations together, I get that Americans consume just over 1,200 billion calories of candy in the weeks prior to Halloween (240 billion 900 billion = 1,210 billion).
From the information provided in the initial question, I know that consuming 3,500 calories equals a 0.45kg increase in weight. Thus, I know that a 1kg weight increase corresponds to approximately 7,800 consumed calories (3,500/0.45=7,778).
I further know that the total amount of calories (1,200 billion) implies that the US population would increase by approximately 150 million kilos in weight (1200 billion / 7,800 = 154 million).
In conclusion, the American population will gain approximately 150 million kilos, or 150 000 metric tons, given a consumption of $2.7 billion worth of candy in the weeks leading up to Halloween.
Assuming $1 gets you 10 candy, $2.7 billion dollars gets you 27 bilion candy.
Assuming each candy gives you 50 calories, 27 billion candy gives you 1.35 trillion calories (I will assume 1.20 trillion calories, though, in case my 50-calories-per-candy estimate is a bit high and to make calculations easier).
1.20 trillion / 3,500 = anywhere from 300 billion – 400 billion.
That’s number of pounds the American population will gain from eating 27 billion candy.
Hi Victor,
My answer is 231 million pounds.
Cost / bag of candy = $5
Average candy / bag = 10
Average cost / candy = $0.5
# of candy = $2.7BN / 0.5 = 5.4 BN
Calories per candy = 150
Total calories = 810 BN
Calories / pound = 3.5 K
Total pounds = 810 BN / 3.5K = 231 M
Pounds / person = 231 / 320 = 0.723 lbs
— Seems reasonable
Weight Gained:
246.78 Million lbs. or 111.051 Million KGs
How:
As per various statistics about preferred holiday candy in the US, candy consumption is estimated at 70% chocolate based and 30% non-chocolate based. The split in the candy variety in the picture above is similar to these estimates.
Prices below based on average from 3 major retailers and calories based on sample of popular candies in the US.
Also, prices vary 10-20% between retailers. Calories by grams/oz vary significantly for some types of candy. Ignoring these, we estimate weight gained as follows:
Chocolate (C) based: 382 calories per $1
Non-chocolate (NC) based: 175 calories per $1
Calculation:
C = $2.7B * 70% * 382 = 721.98 Billion Calories
NC = $2.7B * 30% * 175 = 141.75 Billion Calories
Total Calories = 863.73 Billion Calories
Conversion:
Pounds = 863.73 / 3500 = 246.78 Million lbs.
KG = (863.73 / 3500) * 0.45 = 111.051 Million KGs
Assumptions made:
1. Each piece of candy is 100 calories
2. There are 25 pieces of candy per bag
3. Each bag costs $5
If $2.7billion was spent on candy, it would suggest about 540,000 bags were sold. At 25 pieces per bag we would have about 13,500,000 total pieces. At 100 calories/ piece there would be a total of 1,350,000,000 calories consumed. If we Americans (present company included due to trick or treating tax as well) gain 1 lb per 3500 calories we, as Americans, would have gained a total of ~385,000 lbs.
On a per per person basis, assuming there is 325,000,000 people in America, it would be about 0.001 lbs per person (on average).
A bit more than 165 million lbs in total.
Thought process:
Estimate of the calories per 100g of candy : 450cal
Estimate of the price per 100g of candy: 2.1 $
2.7 billion / 2.1 = ~1.3 billion (of 100g packets of candy)
1.3 billion * 450 cal = 578 billion (total calories)
578 billion / 3500 = 165 million lbs
If we consider that the US population is about 319 million, that’s about 0.5 lbs per person (230g). But the candy is not divided equally among people, so…!
Total spent:
$2.7 B
A pound of candy price:
$0.65/lb
Total amount of candy:
$2.7 B/($0.65/pound) = 4.15 B lb
Let’s use chocolate as a proxy for all candy:
2425 cal/lb
Total calories consumed:
4.15 B lb*2425 cal/lb = 10,067 B cal ≈ 10 T cal (T = 10^12)
Pounds gained:
10 T cal / (3500 cal/lb) = 2.86 B lb ≈ 2.9 B lb
FINAL ANSWER:
2.9 B lb
—
If we compare this to the American population (≈320 M), that means that every American on average gain ≈ 90 lb…