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”
Step 1: Convert revenue into candy bags
Assume all candy is purchased in bags, and can be segmented into chocolate and non-chocolate. At a price of $27 per bag for a jumbo-size bag of each type, we have:
Number of bags = Candy revenue/bag price =
$2.7b/$27 = 100m bags.
Assume 50% of candy is chocolate and 50% is non-chocolate.
Bags in chocolate = number of bags * bag percentage = 50% of 100m = 50m chocolate bags, and 50m non-chocolate bags.
Step 2: Weigh the bags.
Assume that non-chocolate bags weigh 6 lbs. each (reference at bottom of comment) and chocolate bags weigh approximately 4 lbs. each.
Non-chocolate weight = weight per non-chocolate bag * bags = 50m bags * 6 lbs./bag = 300m lbs.
Chocolate weight = weight per chocolate bag * bags = 50m bags * 6 lbs./bag = 200m lbs.
Step 3: Segment weight into fats, sugars, and fillers.
Doing research into various candy types, and using the formulas:
weight% in fat = fat weight in grams/serving weight in g
weight % in sugar = sugar weight in grams/serving weight in g,
assume an approximate segmentation for chocolate of 20% fat, 75% sugar, and 5% filler with no nutritional value. Assume that non-chocolate can be segmented into 80% sugar and 20% filler.
Chocolate fat lbs. = chocolate fat% * chocolate weight = 20% of 200m = 40m lbs. of fat
Chocolate sugar lbs. = chocolate sugar% * chocolate weight = 75% of 200m = 150m lbs. of chocolate sugar
Non-chocolate sugar lbs. = non-choc sugar% * non-sugar weight = 80% of 300m = 240m non-chocolate sugar lbs.
Total fat weight = Chocolate fat weight = non-chocolate fat weight = 40m lbs. chocolate 0 lbs. non-chocolate = 40m lbs.
Total sugar weight = Chocolate sugar weight non-chocolate sugar weight = 150m lbs. 240m lbs. = 390m lbs. sugar
Step 4: Convert to grams, using 454 g per lb.
Fat grams = 454 g/lb * fat lbs. = 454 g/lb * 40m lbs. = 18b g fat
Sugar grams = 454 g/lb * sugar lbs. = 454 g/lb * 390 m lbs. = 450 g/lb * 400m lbs. (est.) = 180b g sugar consumed
Step 5: Convert to calories
Fat has 9 calories per gram, sugar has 4 calories per gram.
Fat calories = 9 cal./g * fat g = 9 cal./g * 18b g = 160b cal. (Est.)
Sugar calories = 4 cal./g * sugar g = 4 cal/g * 180b g = 720b cal.
Total calories = total fat calories total sugar calories = 160b fat cal. 720b sugar cal. = *** 880b total calories ***
Pounds gained = total calories/calories per pound = 880b calories/3500 calories per pound = *** 250m lbs. gained! (Est.) ***
Reasonableness: As there are 300 million Americans, each American gains just under one pound from eating sugar on the holiday, which seems sensible.
Chocolate bag source: 62.6 oz bag of “Mars Mix” on Quill
Non-chocolate source: Candy Warehouse “Funhouse Treats Assorted Candy Mix”
Based on average calorie per candy (http://edition.cnn.com/FOOD/resources/food.for.thought/sweets/compare.candy.bar.html) it works out to be 239 calories on average. (total items divide by total calories..sorry lost my page but its roughly 9500/41)
and Similary average price of candy based on information from here http://www.candywrapperarchive.com/candy-collector/candy-prices-over-the-years/ and here
http://247wallst.com/special-report/2012/04/05/americas-favorite-chocolate-brands/2/) works out to be 1.30 per candy
Now that means that 239 calories = 1.30 dollars
which means 2.7 billion dollars create 239/ 1.30 x 2.7 billion=
= 496.3846 billion calories
Now if 3500 calories create a weight gain of 1lb, total weight gain is 496.3846/3500 billion lbs or 141824175.841 lbs for the population
Total Spent on Candy: $2,700,000,000
Cost Per Bag (80 pieces): $10
Total Bags Sold: 270,000,000
Pieces Per Bag: 80
Total Pieces Sold: 21,600,000,000
Avg Calories Per Piece: 60 cals/piece (most fun size candy is between 35 and 85 calories)
Total Calories: 1,296,000,000,000
Calories Per Pound: 3,500 cals/lb
Total Pounds Gained if all candy is consumed: 370,285,714 lbs
Assuming a population size around 325 million individuals, that’s over 1.1 lbs per person in candy. Scary to think about given that the other “eating” holidays are right around the corner.
The Americans purchased $2.7Bn of candy.
Let’s assume that the average candy costs $1.35 per candy. Hence, a total of 2Bn candies were sold during this time period. Further, on average, assuming that each candy contains approx. 140 calories. Hence, the candies sold contain a total of 280 Bn calories, which leads to a total of approx. 80 Million pounds of weight increase.
Assuming the US population is 200 Million, the average weight increase due to this is 0.4 pounds or 180 grams per person, which seems a fair number assuming these calories are not burnt in activities or utilized.
Let’s assume there are CANDY A and CANDY B.
Let’s assume CANDY A is 1000 calories and costs 1$ and CANDY B is 2000 calories and costs 2$. Let’s assume the sales of the two types of candy are equally shared (50% A, 50% B).
The total amount of calories “collected” by US children during Halloween was
TOTCAL(A)= (0,5 x 2,7 billion$)/1$ x 1000 calories = 1,35 billion kcal
TOTCAL(B)=(0,5 x 2,7 billion$)/2$ x 2000 calories = 1,35 billion kcal
TOTCAL(A B)= 2,7 billion kcal
Let’s assume all the US parents tax their children at a 33% tax rate like you, that means a total effective calories (TOTEFFCAL) available of
TOTEFFCAL= (1-0,33) x 2,7 billion kcal = 1,81 billion kcal
If 3,5 kcal = 1lb of weight gained, that means a total gain in weight of
TOTGAIN= (1,81 billion kcal)/3,5 kcal =0,52 billion lb
That means a gain of 0,52 billion lb x 0,45 kg/lb = 233 million kg in only one week! (Let’s assume kids will finish their candies within one week)
Let’s assume that kids (until 15 years) are 20% of the entire US population, that means 64 million of kids.
That means 233 million kg/64 million kids =3,64 kg per kid.
Oh, I finally understood how US population has a 40% of obesity rate.
Total weight gained by American population = 515 Million Pounds.
$2.7B in Candy
Cost of Average Pack of 200 pieces candy – $12
Each piece of candy has – 40 Calories
Total number Candy = 2.7B / 12 $ = 0.225 B = 225 million * 200 = 45000 = 45 Billion pieces of Candy
Total Calories = 45Billon * 40 = 1800 B calories
Required Calories to gain 1 pound – 3500 Calories
Total weight gained by 1800 B calories = 1800 Billon Calories / 3500 = 515 Million Pounds.
Step 1: Begin with $2.7 billion dollars.
Assume that all candy is purchased in bulk bags, noting that the picture has fun-size candy pieces and homeowners will likely avoid purchasing full-size candy bars due to price, and that 50% of candy consumed is chocolate and 50% is non-chocolate.
Two bags that I found that had a wide variety of candies available were sold at just under $27 per bag, citing the following:
Non-chocolate: http://www.candywarehouse.com/products/funhouse-treats-assorted-candy-mix-175-piece-bag/
Chocolate (note that this is Mars brand):
http://www.quill.com/chocolate-candy/cbs/342139.html?hidedisruptive=1&cm_mmc=SEM_PLA_NULL_342139&mcode=SEM_PLA_NULL_342139&gclid=CNrO6bWQiNACFUMDhgod3wMGfg
The formula used to estimate the number of bags is:
Number of bags = Total candy sales/price per candy bag
At an estimated price of $27 per bag applied to $2.7 billion in candy sales, this leaves a figure of 100 million bags, with 50 million sold in non-chocolate and 50 million sold in chocolate.
Step 2: Using the figures listed for each bag as a baseline, note that the non-chocolate bag has an average weight of 6 lbs. and the chocolate bag has an average weight of approximately 4 lbs. Assume that all weight is candy only and that the weight of packaging is insignificant.
Using the formula:
Total candy weight = Weight of bag * number of bags,
We get
Non-chocolate weight = 6 lbs./bag * 50m bags = 300m lbs.
Chocolate weight = 4 lbs./bag * 50m bags = 200m lbs.
Step 3: Assume that candy, as a form of junk food, has no protein. (Because protein and sugars both have 4 calories per gram, these categories could be considered as one from a purely computational perspective) Use nutritional data from full-size candy bars to segment the weight of candy into fats and sugars.
Using research from the websites of Snickers, 3 Musketeers, and Twix as a baseline, and looking at total weight in grams of fats and sugars on the labels, as opposed to weight of the candy itself (using the formula weight% in fat = total grams of fat/total grams of product), assume that these candies have approximately 20% of their weight in fat and 75% of their weight in sugar, with 5% to other ingredients with no nutritional value.
Using similar data for various non-chocolate candies, assume that 80% of their weight is in sugar with 20% devoted to ingredients with no nutritional value.
Then:
Choc. fat weight = weight% in fat * choc. weight
Choc. sugar weight = weight% in sugar * choc. weight
Chocolate fat weight = 20% of 200m lbs. = 40m lbs.
Chocolate sugar weight = 75% of 200m lbs. = 150m lbs.
Non-chocolate sugar weight = weight% in sugar * non-choc. weight
Non-choc sugar = 80% of 300m = 240m lbs.
Then:
Total fat weight = Total choc. fat weight (as non-choc weight 0%) = 40m lbs.
Total sugar weight = choc sugar weight non-choc sugar weight = 150m lbs. 240m lbs. = 390m lbs.
Step 4: Convert weights to grams, knowing that there are approximately 454 grams in one pound…
Fat weight in grams = grams/lb * lbs. = 454 g/lb * 40m lbs. = 18b grams of fat (estimation)
Sugar weight in grams = grams/lb * lbs. = 454 g/lb * 390m = 450 g/lb * 400m lbs. (estimation) = 180b grams of sugar.
Step 5: Calculate total calories, knowing that fat has 9 calories per gram and sugar has 4 calories per gram.
Fat calories = cal./gram * grams = 9 cal./gram * 18b grams = 160b calories (estimation)
Sugar calories = cal./gram * grams = 4 cal/gram * 180b grams of sugar = 720b calories
Total calories consumed = fat calories sugar calories =
160b calories 720b calories = *** 880b calories ***
Total pounds gained = calories consumed / calories per pound =
880b calories / 3500 calories per pound = *** 250m lbs. gained! (Estimation) ***
For reasonableness, assume that as there are approximately 300 million Americans, each American gains just under one pound in candy consumed on Halloween, which seems sensible given the circumstances.
The American population will gain 55,028,571 pounds from eating $2.7B in candy based on the following assumptions:
$4 / per bag of candy
428 calories / per bag of candy
Adults consume 1/3 and kids consume other 2/3 of candy
Adults gain 1 pound from 3,500 calories
Kids gain 1 pound from 7,000 calories
Assume each $1 can buy chocolate that has 500 calories.
$2.7 bn/500/3,500 = 1,543 pounds
the American population will gain 1,543 pounds from chocolates only.
Total Candy sales = USD 2.7 Bn
Assuming people buy candy in boxes.
Price per box = USD 9.2 (Price based on conversion factor of 1 USD = 1.3 CAD)
http://www.walmart.ca/en/ip/cadbury-maynards-assorted-fun-treats-candy/6000196255821
Candy/box = 80
Calories/candy = 60 calories
Calories/box = 4800 calories
No of boxes for USD 2.7 Bn sales = 293,478,261
Calories for 293.48 Mn boxes = 1.4 Trillion calories
Assuming, there is a 33% tax by all parents (like you) and that 33% candy is discarded.
Total Calories consumed = 1.4 trillion (1-33%)
= 943.82 Bn calories
3500 calories to gain 1lb (0.45 Kg)
Total weight gained = 269.67 Mn pounds
= 121.34 Mn Kgs