Candy Hearts + Math = Prize!
February 8, 2022 9:17 AM Subscribe
The three closest guessers in my apartment building's contest will win gift cards to our neighborhood co-op grocery. How can I figure out how many candy hearts are in the container?
Here are two really bad photos taken through the glass to the display in the apartment office. The sign to the left of the jar is printed on a standard 8.5x11 inch sheet of paper. The jar itself looks to be about 12-ish inches high and maybe 6-ish inches in diameter? The candies are the standard sized candy hearts with trite sayings on them. How do I figure out how many of them are in the jar?
Here are two really bad photos taken through the glass to the display in the apartment office. The sign to the left of the jar is printed on a standard 8.5x11 inch sheet of paper. The jar itself looks to be about 12-ish inches high and maybe 6-ish inches in diameter? The candies are the standard sized candy hearts with trite sayings on them. How do I figure out how many of them are in the jar?
Buy a pack of candy hearts - enough to fill a measuring jug. Divide the number of hearts in the container by the volume of the container.
Work out the volume of the jar, based on the height and internal diameter. Multiply by the number you obtained in your experiment. That should give you a close approximation (say, within 5%) of the number in the jar.
posted by pipeski at 9:35 AM on February 8, 2022 [14 favorites]
Work out the volume of the jar, based on the height and internal diameter. Multiply by the number you obtained in your experiment. That should give you a close approximation (say, within 5%) of the number in the jar.
posted by pipeski at 9:35 AM on February 8, 2022 [14 favorites]
I saw some television program where a group of children were guessing how many jelly beans were in the jar, and when they averaged all of the guesses it was surprisingly close to the true value. So, perhaps crowdsource the effort?
posted by sacrifix at 9:53 AM on February 8, 2022 [4 favorites]
posted by sacrifix at 9:53 AM on February 8, 2022 [4 favorites]
I would do:
assume a cylinder
count how many candy hearts extend from centre to edge assuming a flat orientation
square this and multiply by pi (thus pi-r-squared)
multiply by the number of candy hearts in the flat orientation that make the height (pi-r-squared-h, a cylinder)
the packing efficiency of random objects is about 60%, so multiply by 0.6
posted by wattle at 10:36 AM on February 8, 2022 [2 favorites]
assume a cylinder
count how many candy hearts extend from centre to edge assuming a flat orientation
square this and multiply by pi (thus pi-r-squared)
multiply by the number of candy hearts in the flat orientation that make the height (pi-r-squared-h, a cylinder)
the packing efficiency of random objects is about 60%, so multiply by 0.6
posted by wattle at 10:36 AM on February 8, 2022 [2 favorites]
Get someone who likes to count stuff count them by hand (use gloves). I would do it!
posted by a humble nudibranch at 10:46 AM on February 8, 2022 [1 favorite]
posted by a humble nudibranch at 10:46 AM on February 8, 2022 [1 favorite]
Response by poster: as it's a guessing contest, we're not allowed to measure, touch, or count the contents of the jar.
posted by QuakerMel at 10:52 AM on February 8, 2022 [1 favorite]
posted by QuakerMel at 10:52 AM on February 8, 2022 [1 favorite]
Having seen it, what do you estimate it weighs?
A 14 oz bag of Brach's hearts is said to have 26 servings of 11 candies (~286 per bag).
So, a 5 lb bag of candies would be about 1634 candies.
You could also stop in the nearest stores that sell candy hearts to look at the bags and estimate how many the office purchased.
posted by xo at 10:58 AM on February 8, 2022 [6 favorites]
A 14 oz bag of Brach's hearts is said to have 26 servings of 11 candies (~286 per bag).
So, a 5 lb bag of candies would be about 1634 candies.
You could also stop in the nearest stores that sell candy hearts to look at the bags and estimate how many the office purchased.
posted by xo at 10:58 AM on February 8, 2022 [6 favorites]
If we're crowsourcing the guess as noted by sacrifix above, my estimation is closer to 2500.
posted by hydra77 at 11:01 AM on February 8, 2022 [1 favorite]
posted by hydra77 at 11:01 AM on February 8, 2022 [1 favorite]
You could also stop in the nearest stores that sell candy hearts to look at the bags and estimate how many the office purchased.
While wattle's answer is the "correct" one (and pretty easy to derive just from the photos), this is the right one. Given that it's not filled to the top, they probably bought two or three big-ass bags of hearts and dumped them in.
posted by uncleozzy at 11:04 AM on February 8, 2022 [7 favorites]
While wattle's answer is the "correct" one (and pretty easy to derive just from the photos), this is the right one. Given that it's not filled to the top, they probably bought two or three big-ass bags of hearts and dumped them in.
posted by uncleozzy at 11:04 AM on February 8, 2022 [7 favorites]
Agreed with the above. As a packing problem you can work out on paper, this is really hard. If you like candy hearts or wasting a few dollars, fill a measuring cup ten times with one bag and take an average of the volume.
posted by eotvos at 11:22 AM on February 8, 2022 [1 favorite]
posted by eotvos at 11:22 AM on February 8, 2022 [1 favorite]
The only possible problem with all of the proposed solutions: all of these methods/calculations are based on the assumption that the jar contains only candy.
So.. What if there is a non-candy object in the jar hidden in the middle of the candies?
posted by RobinofFrocksley at 11:34 AM on February 8, 2022 [4 favorites]
So.. What if there is a non-candy object in the jar hidden in the middle of the candies?
posted by RobinofFrocksley at 11:34 AM on February 8, 2022 [4 favorites]
Response by poster: What if there is a non-candy object in the jar hidden in the middle of the candies?
I think we can assume good intent on the part of the apartment staff and base the calculations/guesses on a jar full of (only) one type of candy.
posted by QuakerMel at 12:00 PM on February 8, 2022 [2 favorites]
I think we can assume good intent on the part of the apartment staff and base the calculations/guesses on a jar full of (only) one type of candy.
posted by QuakerMel at 12:00 PM on February 8, 2022 [2 favorites]
Curious George tackled this question on the episode "Fun-Ball Tally" by filling a similar-sized jar with similar sized objects.
posted by ewok_academy at 12:20 PM on February 8, 2022 [1 favorite]
posted by ewok_academy at 12:20 PM on February 8, 2022 [1 favorite]
Welll. I counted 14 blobs across and 23 blobs vertical. Using the wattle formula π.r2. h this gives my best guess N = 3540. To get a handle on my confidence in this answer, I went high 15 x 24 = 4240 ; and low 13 x 22 = 2920. Your best strategy, following Francis Galton's ox-weight guessing, is to take the average of all the actual punts in this thread. Actually, xo might be on to something: 2x 5lb bags falls within my range, so N = 3270 could be upweighted.
posted by BobTheScientist at 1:12 PM on February 8, 2022 [4 favorites]
posted by BobTheScientist at 1:12 PM on February 8, 2022 [4 favorites]
I second sacrifix... this is actually a well-known and well-studied phenomenon in cognitive science known as the Wisdom of Crowds. The basic idea is that for something like this (guessing the number of items in a jar), everyone's guess is a combination of signal (i.e., the data they see about the jar) + noise (i.e., error)... but across people, the signal is the same and the noise (errors) is randomly distributed. What that means is that if you get a lot of independent estimates, the errors cancel each other out, and the signal remains: so averaging lots of those estimates tends to be quite accurate.
Key to making this work is that the estimates have to be independent, i.e., made without knowing what other people were estimating (otherwise the errors are correlated and don't cancel). So, averaging people's guesses here in this thread won't work, but if you asked a bunch of people individually and averaged that, it probably would.
posted by contrapositive at 3:41 PM on February 8, 2022 [4 favorites]
Key to making this work is that the estimates have to be independent, i.e., made without knowing what other people were estimating (otherwise the errors are correlated and don't cancel). So, averaging people's guesses here in this thread won't work, but if you asked a bunch of people individually and averaged that, it probably would.
posted by contrapositive at 3:41 PM on February 8, 2022 [4 favorites]
My counts, done independently of BobTheScientist are shown here; I got 27, 23 and 23 vertical (left to right) and 16, 20, 16 horizontal (top to bottom). This produces estimates of 24.3 by 17.3, which is 5742 hearts. My counts show some variance, a standard deviation of around 2.3 hearts; assuming no correlation, that means that there's a 50% chance the value is between around 4400 and 7100, and an 80% chance between 3500 and 8750.
posted by Superilla at 4:04 PM on February 8, 2022 [2 favorites]
posted by Superilla at 4:04 PM on February 8, 2022 [2 favorites]
Ok, I’m bad at math BUT I think there are 4,902 candy hearts in the jar. I am basing this off of a) my own attempt at counting and wattle’s formula, and by googling to see what a 5 lb pound bag of hearts looks like size wise. They come in a gallon sized bag, and to me your photo looks it holds 3 gallons, which would be the 4902 which is close to the 5000-6000 I was hitting with my (probably shoddy) math.
Interestingly, we just had this contest at work but with chocolate kisses. I did not enter but I asked the woman who won what her strategy was and she said she hung out and eavesdropped on other people guessing and then took their average, so wisdom of the crowd is a solid way to go here. Let us know the results!
posted by nancynickerson at 4:40 PM on February 8, 2022 [4 favorites]
Interestingly, we just had this contest at work but with chocolate kisses. I did not enter but I asked the woman who won what her strategy was and she said she hung out and eavesdropped on other people guessing and then took their average, so wisdom of the crowd is a solid way to go here. Let us know the results!
posted by nancynickerson at 4:40 PM on February 8, 2022 [4 favorites]
I think it's also a very safe assumption that the organizers did not actually count the number of candy hearts and are themselves using the estimate provided on the packaging containers.
posted by LKWorking at 12:53 PM on February 10, 2022 [1 favorite]
posted by LKWorking at 12:53 PM on February 10, 2022 [1 favorite]
This thread is closed to new comments.
posted by QuakerMel at 9:21 AM on February 8, 2022