Can you solve the 4 foods puzzle?

Рет қаралды 267,918

7 ай бұрын

Thanks to James W. for the suggestion! At an amusement park, 65% of visitors ate a donut, 80% ate a soft pretzel, 80% ate pizza, and 90% ate ice cream. What is the minimum percentage of visitors that ate all 4 foods?
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Пікірлер: 566

@thewordsmith7364 7 ай бұрын

I solved it by inverting the percents (100-p)%, then adding it together, to figure out what percentage at most didn’t eat at least one food

@Noname-67 7 ай бұрын

Best solution

@leonais1 7 ай бұрын

You can make that mathematically sound by showing that the minimum percentage goes up if there are overlaps between the people who don't eat each food. It's still the best way though.

@mihailghinea 7 ай бұрын

same!

@Sonny_McMacsson 7 ай бұрын

Or add them together and do (mod 100).

@danfg7215 7 ай бұрын

I did the same thing and arrived at 15%, but since I did it "intuitively", I didn't have confidence in the result.

@KroganCharr 7 ай бұрын

For the practical application, you actually do NOT want to target the people who bought all 4. Bundles are typically cheaper than the sum of the individual items - that's the point of the bundle. If we only sell the bundle to people who bought all 4 anyway, we just lose money. The people we ACTUALLY want to target are the ones who bought less, but might be convinced to buy all 4. Most likely, the people who usually buy 3 out of 4 could be tempted by a bundle offer. The donut merchant would be the most likely to profit from this, as most people who only skipped out on 1 probably skipped the donut.

@TheBlobik 7 ай бұрын

The information request is still useful though. We know, that with such bundle we loose with at least 15% of the customers, and up to 65%. So, looking for info about people who bought all 4 makes sense, but we should focus on the maximum number of people who did that. Then we can set up the pricing in such way, that even in worst case scenario extra spending of the part of 35% of customers will make up for the loss on 65%. This is of course a "safe bet" scenario, most companies probably could tolerate some risk and look for "most likely % of people who bought all 4" to use in estimations instead.

@willguggn2 7 ай бұрын

@@edsimnett The four numbers most certainly aren't independent variables. People have preferences and don't truly randomly buy food in the real world. Upper and lower boundaries however still apply.

@Tiqerboy 7 ай бұрын

You also have to measure the time people bought items. If people bought all four at once or 3 items at once (usually a family) that's different than an individual buying all four items but over a longer period of time.

@DemPilafian 7 ай бұрын

Keep in mind that the *_"geniuses in marketing"_* was meant sarcastically.

@Patrik6920 7 ай бұрын

@@willguggn2 true, and for a small sampling ..not very informative ..but on a larger sampling .. the errors smooth out... as in the exaple lets assume 20 ppl...the variance from day to day will be massive if we say saple 20000/day for a week ... i would say the error becomes so small .. we can with a quite high degree of certainty predict the sales... in the future... and what prferences ppl have .. we can then add other factors as weather, pricing etc... ...we can also just by using common sense do estimations (if its 10 deg and windy, the probability our outdoor ice cream stand sell alot of icecream is quite low)

@ZekeRaiden 7 ай бұрын

Minimum percentage can always be determined by picking the lowest percentage (in this case, 🍩 at 65%), and then subtracting away all the "did not eat X" percentages. In this case, those are 20%, 20%, and 10%, for a total of 50%. 65% - 50% = 15%. The actual amount that ate all four items is probably higher, up to maximum of the lowest percentage, 65%.

@knoxiegb1782 7 ай бұрын

Yeah I remember being in school and struggling with a variation of this problem. Is there any flaw with that reasoning?

@opinionhaver574 7 ай бұрын

That's how I solved it.

@emulgatorx 7 ай бұрын

You don't have to start with the lowest percentage, any of them work as a starting point.

@ZekeRaiden 7 ай бұрын

@@knoxiegb1782 Formally speaking, what I did was just a specific application of the proof given near the end of the video. The union of WXYZ is no smaller than the whole space (100 percentage points) minus the complement of each individual set. Thing is, (whole space) - (complement of set W) = the set W, by definition. You can, as other replies have said, pick any starting point. I just find it most natural to start from the smallest one first.

@donaldhobson8873 7 ай бұрын

max(0,100-sum(100-x for x in percentages)) simpler.

@AgusSkywalker 7 ай бұрын

The easiest way is calculating the inverse. The max amount of people that didn't eat all 4. You just add the percentages of people who didn't eat each food. 10 for ice-cream, 20 for pretzels and pizza, and 35 for donut. 10+20+20+35=85, which means at most 85% didn't eat all 4 foods, so at least 15% had to eat all 4.

@onradioactivewaves 7 ай бұрын

Nice, but don't forget to also limit the answer to between 0-100% .

@RoderickEtheria 7 ай бұрын

If it exceeds 100% subtracted, you can state that there is no portion of the populace that guaranteed ate all types of food.

@ShaiFishman 7 ай бұрын

Exactly! @@RoderickEtheria

@bharathram7245 7 ай бұрын

@@ShaiFishmanwow i would have missed good content if i haven't come through comment section 😄

@breathless792 7 ай бұрын

this is how I solved it

@g.c.9904 7 ай бұрын

I can never solve the puzzles in the channel because when I open the video the solution is right in front of me in the top comment.

@Mr_Gamer_123 7 ай бұрын

Those looking for a simpler method: I did this problem instantly in my head. 100-65 = 35, 100-80 = 20, 100-80 = 20 & 100-90 = 10. Add all these numbers up (35+20+20+10) = 85. 100 - 85 = 15%! Explanation: 35% didn’t eat a doughnut, 20% didn’t eat a pretzel etc. So 85% didn’t eat all 4 foods. So 15% did!

@howareyou4400 7 ай бұрын

My elementary school way is the simplest (and also proves it at the same time) * 65% eat A, 80% eat B, so "eat A and B" is at least 65% + 80% - 100% = 45% * now same logic, 45% eat AB, 80% eat C, therefore "eat ABC" is at least 25% * eat ABCD is at least 15% Each step itself also naively proved that it's a reachable lower bound (thus minimum) The calculation is even simpler as: 1. you remove the 100th so it's smaller number 2. you can early exit if the sum is less than 100 and claim that the min is already 0 without adding all other numbers.

@Visstnok 6 ай бұрын

This is the one correct solution.

@oqui7009 5 ай бұрын

I solved it the same way, but I would have put parentheses, otherwise the solution would be unclear without them. We assume that in our group of eaters it is precisely those people who did not eat other food; 65% - (100% - 80%) - (100% - 80%) - (100% - 90%) = 80% - (100% - 65%) - (100% - 80%) - (100% - 90%) = 90% - (100% - 65%) - (100% - 80%) - (100% - 80%) This is basically the same first method from the video... Although the second one is similar. I don’t see any difference between the solutions, we rely on the same thing

@howareyou4400 5 ай бұрын

@@oqui7009 1. 65% - (100% - 80%) is no more clear than simply 65% + 80% - 100%, if you think about it. In fact I believe the entire elementary school "math" stuff is about thinking through these kind of logics. 2. you forgot about the possibility of "early exit". We do not need to write everything down at once. We can do the simple arithmetic in our mind and whenever we get negative number we know it's 0 and there is no need for further calculations.

@kgeiger61 3 ай бұрын

That's how I did it. Took me about 20-30 seconds.

@AncientBulldozer 2 ай бұрын

In the first calculation about "A and B" how did you count for those who didn't eat either A or B ? Its the set intersection formula n(A or B) = n(A) + n(B) -n(A and B). But in this case how can one assume that n(A or B) is infact 100% of the total sample? Also there are a minimum of 10% of total sample who did not eat either A or B

@OOKIEDOKIE 7 ай бұрын

I did it by thinking of a group of 100 people, and taking it at groups of 2 at a time. If you take the first two groups, 80 people had the pretzel, which means minus the 35 that didnt have the donut you still need 45 that did. Then for pizza you take the 55 away that didnt have both donut and pretezel but you still need 25 that had both, so then you need 25 that had all 3. Then for icecream you take 75 away that didnt have all previous 3, but that still leaves you with 15 that did, so atleast 15 had to have all 4.

@mihailghinea 7 ай бұрын

Minimum 15%. Maximum 65%. Expected percent of people to eat all 4 foods 37.44%.

@kennyalbano1922 7 ай бұрын

So that’s what my wrong calculation of 37.44% measured. You’re saying this percent measures the expected percent of people to eat all 4 foods. But why is the expected percent, the minimum percent, and the maximum percent all able to be calculated yet mean different things. I am not sure I actually understand what these three terms means in this contexts. All I know is I had thought I was finding the solution when I multiplied the 4 original percentages together to get 37.44% but found out I was mistaken. The 65% for the maximum makes intuitive sense to me as well I think but I don’t get why the expected is not the same as the minimum in this case?

@WombatMan64 7 ай бұрын

@@kennyalbano1922 Expected is more akin to the average. The minimum is essentially assuming as much as possible that people didn't eat all four and getting the smallest number which satisfies that criteria. Two easy examples to illustrate. If you flip a fair coin 20 times, the expected number of heads is 10. The minimum is 0, and the maximum is 20; both are unlikely, but technically possible. If you roll 2 fair 6-sided dice, the expected total of roll of the dice is 7; as that's what you'll get on average. The minimum is 2, and the maximum is 12. Amusingly the expected roll of a single die is 3.5; even though that's not technically possible.

@kennyalbano1922 7 ай бұрын

@@WombatMan64 are there any ways to measure spread with this type of data. Such as range and outliers, does it follow a bell curve and if so what are its standard deviation and variance? Can the data be described by an equation and displayed graphically? I mean where the 4 foods intersect as in the question by the data.

@WombatMan64 7 ай бұрын

@@kennyalbano1922 not really with only the information supplied. If you had a table with every single customer and exactly what they purchased, and had that info every day then no doubt you could do some good analysis, but the information provided in this question is quite... minimal. Appropriate really.

@thenonexistinghero 7 ай бұрын

@@edsimnett Actually it can be very useful. Businesses work on a daily basis. If you're gonna do business with a company, it's not only important to know how much someone sells on average and how much on the good days, but also how much they sell on the worst days (and also the factors contributing to the lowest and highest sales).

@aididdat1749 7 ай бұрын

I love the videos presenting plenty of methods!

@lefthanded3512 5 ай бұрын

Brilliant video 👍🏻 Thanks for breaking it down and making it easy to understand!! 💯

@TheGraemeEvans 7 ай бұрын

Nice to have an easy problem every so often.

@chinareds54 7 ай бұрын

I approached this by simplifying it to 2 foods. This can be visualized by two sliding bars (line segments) of various lengths which must be positioned in a specific space (100%). How would we minimize the overlap? Easy, we put one bar all the way to one side and the other bar all the way to the other. So for example with Ice Cream (90%) and Pizza (80%), the mininum overlap would be 70%. But now we know a minimum of 70% had both Ice Cream and Pizza, so I can repeat this with the Pretzel (80%). So mininum 50% had Ice Cream/Pizza/Pretzel. Apply this once more with Donut (65%) and the minimum overlap is 15%.

@rolandkraus15 7 ай бұрын

Yes, minimal possible overlap of the two lowest percentages, where you stack one from the "left" and one from the "right". That would also tell you right away, that if two food items were at maximum 50%, the minimum of people who ate everything is 0%.

@rolandkraus15 7 ай бұрын

Actually, if your two items with the lowest percentages would "sum up" and that combined result is less than 100%, your minimal possible overlap would always be 0%. In an extreme example, out of 1000 people you have 999 eating pizza, and 1 person eating brussel sprouts. Those 999 and 1 can be completely different groups of individuals - so you can have 0 overlap. Adding more food items to your combined considerarions here won't have any impact on the overall minimum across ALL food items then.

@Tiqerboy 7 ай бұрын

That's exactly how I did it. Too many smart people in Presh's audience, LOL

@aditya37mviews3weeksago3 7 ай бұрын

I tried to do something similar but my approach was very complicated, I tried to make a square with 10 smaller boxes along each arm, thus 100 of them inside. Then, I tried representing each beverage along each corner to minimize the overlap...but i forgot that the result will be skewed if I used multiple beverages at the same time, I think I had to start with two beverages and put them at the diagonally opposite end then calculate their overlap and continue like you, but yours is much better and simple. Also, what if the percentage of one of the beverages was way less like 2 or 3% then we wouldn't get any overlap, would that mean that but is possible that no one bought all four?

@rolandkraus15 7 ай бұрын

@@aditya37mviews3weeksago3 Yes, if you have one food item with like only 3%, any of the other food items would need to have over 97%, so that there could be a minimal, but none-zero overlap among all.

@NeverMatter 7 ай бұрын

1000th video!! Congrats man!

@Imperial_Squid 7 ай бұрын

I got the first 65% 80% trick to arrive at 45% due to seeing this kind of puzzle but didn't think to extend it out further to all four, cool trick! It's also interesting to note that, so long as each set contains less than 100%, you can keep adding more and more orthogonal sets and eventually arrive at 0% minimum overlap Eg, for sets that contain 50% of a population, you need 2 such sets to have a minimum overlap of 0%, if they cover 75% then you need 4 sets, 90% coverage requires 10 such sets, etc etc but however many ways you have of grouping people, so long as you have enough of them you'll be able to show that the minimum possible overlap is 0%

@gblargg 7 ай бұрын

I loved seeing it worked in many different ways. This is the real skill, being able to approach things in multiple ways and gauge which one will be simplest.

@swordgeo 6 ай бұрын

I tried at first to follow the method of option A with weird bar graphs but gave up and found myself doing naturally going with option B. I wondered if I had the right idea pairing donuts with pretzels and pizza and ice cream but it seemed to make sense to me. And I'm glad the video showed that I was right!

@mike1024. 7 ай бұрын

This was a great problem! Simple to describe yet still challenging.

@mthielssalvo 7 ай бұрын

neat problem with many ways to solve! i drew the sample space as a 4 by 5 grid, such that every cell in the grid represented 5%. I then filled the grids with markers for each food, each time adding the nth food starting by avoiding the cells that already had (n-1) foods in them. this leaves only three of the 20 cells with all four markers!

@jonahcomstock3061 6 ай бұрын

I did exactly this!

@ValleysOfRain 7 ай бұрын

This is basically gerrymandering for food groups.

@ladylaylowjk 7 ай бұрын

Solved in 3 mins.. very satisfied, thank you! I solved by considering how many % of all people ever tried one of the food, then 2, then 3 and finally all 4.

@mark91345 7 ай бұрын

After my headache subsides, I'll watch this video again and see if I can follow the logic this time.

@Yusso 7 ай бұрын

I did the second method but then I realized it's easier: Assuming that there are 100 people and no person ate the same item twice. If all of them ate all 4 items there would be 400 sales. But if we add up the numbers there has been 315 sales. So at most 85 people did not eat all 4 items. That means at minimum 15 people ate all 4 items.

@metamud8686 7 ай бұрын

> no person ate the same item twice. The thing is, in the problem description this is left implicit. Somewhere while explaining the answers, this assumption was suddenly put into place. Before that, nobody excluded a person eating, say, 4 slices of pizza.

@Yusso 7 ай бұрын

@@metamud8686 Right. But maybe it's not important how much one person bought of each item. So for example if a person buys 1 donut or 10 doesn't matter. The question then would be, did they buy it or not.

@wafflesaucey 7 ай бұрын

I figured out something sort of like methods 1 and two combined 2 myself, but didn't do the math right. Also, I have to say that I used to watch your videos when I was probably 8-9 (I'm 14 now), and they have not decreased in quality or consistency at all since then. I appreciate the break from brainless youtube content that your videos offer.

@b_ru 4 ай бұрын

Here's what I did: 65% (Donut) + 80% (Pretzel) = 145%. 145% - 100% = *45% of people who ate a Donut/Pretzel ate both of them.* 45% (Donut+Pretzel) + 80% (Pizza) = 125%. 125% - 100% = *25% of people who ate a Donut, Pretzel, or Pizza ate all 3 of them.* 25% (Donut + Pretzel + Pizza) + 90% (Ice Cream) = 115%. 115% - 100% = *15% of people who ate any of the 4 foods ate all 4 of them.* Therefore, at least 15% of customers must have eaten all four foods.

@NesrocksGamingVideos 7 ай бұрын

I usually don't do this, but solved it in less than 10 seconds. More of a logic puzzle than math.

@cedricdrahelia3337 7 ай бұрын

35% didn't eat a donut, 20% didn't eat a pretzel, 20% didn't eat a pizza, 10% didn't eat an ice cream. Worst case scenario : they are not the same people, therefore 35 + 20 + 20 +10 = 85% of people didn't eat one item, so 15% ate all 4.

@XTheSoccerLoverX 7 ай бұрын

Seems like a great problem to illustrate key ideas like DeMorgan's law and the Union Bound, but I don't think the connection was made as clearly as it could have been. There's a lot of intuition that was brought out be each solution, I think the connection to formalized concepts could have been a lot stronger.

@guyhoghton399 7 ай бұрын

The "No Doughnut" set contains 35% of the visitors. "No Pretzels" has 20% of them, "No Pizza" has 20% and "No Ice Cream" has 10%. Anyone not in any of those sets must have bought all four foods. To minimise these people you need to maximise the numbers in the above-mentioned four sets, and to do that you need to assume no sharing of people between them. In that case you simply sum the sets' percentages to get the total %age of visitors that did not buy all four foods, because in doing so no one gets counted twice: 35+20+20+10 = 85. Therefore 15% bought all four foods in this extreme case.

@GS-td3yc 7 ай бұрын

i took two items and took the inverse of the bigger and subtracted from the smaller. substituting the result and repeating yielded 15 percent. after i saw that any order yields the same solution, i am pretty confident

@feynthefallen Ай бұрын

Wow. That was more involved than I expected from my rule-of-thumb estimation.

@soilsurvivor 2 ай бұрын

You're third method is a good illustration of the pidgeon-hole principle. Nice!

@-ZH 7 ай бұрын

Well, this was an easy one. Just imagine each one of the non-eaters don’t overlap, so its just 100%-35%-20%-20%-10%=15%

@ShawnF6FHellcat Ай бұрын

I either got lucky or found a much easier way to do this: -Adding up the percentages of those that didn't eat each food equals 85%. -Subtract that answer from 100%, which equals 15%. I can't explain why that worked, but it apparently did.

@apurbamazumdar968 7 ай бұрын

Fantastic solution, esp. the second way.

@RossBraccoMusic 7 ай бұрын

From a marketing perspective: if on average everyone is already buying at least three food items, there’s really no need to offer a combo discount.

@WombatMan64 7 ай бұрын

Maybe, unless part of the goal is to encourage those who were getting just three items to "just pay a little bit extra" to get all 4. Particularly if the difference between 3 items and the discounted 4 items is more than the unit cost.

@Inspirator_AG112 7 ай бұрын

Another shortcut... *Sum, then subtract 300%.*

@trwn87 3 ай бұрын

Solving a problem of 4 foods in 4 different ways is just too fitting! 😁

@kalan4787 6 ай бұрын

Intuitive answer is 15%. There is an algorithm to execute which makes this exceptionally easy. Basic description: You take the two lowest percentages to start. You have to calculate their intersection so that is going to be 65-(100-80)=45 then you take that answer and intersect the 3rd. 45 - (100-80) = 25 Take that number and intersect the 4th. 25 - (100-90) = 15. Done; it should take you approximately 3 seconds to do in your head. Algorithm: var accumulator = 0 foreach(var p in list){ if accumulator ==0 accumulator = p else accumulator -= (100-p) } accumulator will contain the intersection as long as there is one. A defense is necessary to prevent a disjoint set from resetting the accumulator to a positive number, but I'm not presenting this as a general solution to the problem of all intersecting sets. You have to sort them lowest to highest. It would have been a better problem if he had presented them out of sort order

@doodlePimp 7 ай бұрын

42 seconds in. "Amusement park: What is the minimum percentage of visitors that must have eaten all 4 foods?" 0% Odds are some did not buy any food. - Solved!

@natalieeuley1734 7 ай бұрын

I had all these ideas in my head as ways to solve it, and 15% was my instinct. I just had trouble executing/making it happen 😅

@cnettrouer 7 ай бұрын

I don't solve many of the daily puzzles, but this one came easy for me.

@zettyotta137 7 ай бұрын

couldnt you make a case where everyone that had a donut never ate anything else or the same case with any other type of food or is that getting outside of probabilities?

@matthewwriter9539 7 ай бұрын

I just saw a video with a math puzzle on it. At the top of a paper write "I have $50" Now divide the paper into two columns, Spent Balance 20. 30 15. 15 09. 06 06. 00 For each of these you spend some amount of money, then you write your new balance in the balance column. Now total up each column. The spent adds up to 50, which we expected. Yet the balances all add up to 51...where did that extra one dollar come from?

@mongoliacomix 6 ай бұрын

Using the pigeonhole principle is trivial. Use a 100 cells pigeonhole, now distribute 80 pretzels, 80 slizes of pizza, 65 donuts and 90 icecreams and look for how many cells have necessary the 4 items

@keqling7086 6 ай бұрын

amazing explication! i will definitely write all these methods down as they will help me a lot in exams

@Zykked 7 ай бұрын

Got it right, thought my solution was too simple and that I must have missed something, thought about it for five more minutes, and gave up

@catkook543 7 ай бұрын

another simple way to calculate it. First pick a starting food, and keep that percentage of people who had it. Then list out the percentage of people who havent eaten any of the other given foods. From there, just start subtracting. 65% of people ate a donut 20% of people did not eat a donut (65-20=45) 20% of people did not eat a pizza (45-20=25) 10% of people did not eat a ice cream (25-10=15) There for, the answer is 15%

@h4ck314 7 ай бұрын

Went straight with your last solution.

@maynameismay 7 ай бұрын

I always thought you solved these rather inconveniently... But I suppose a mathematical answer is of greater value than that of an intuitive one, so I'll give you that.

@donsimon2830 5 ай бұрын

I can imagine an ice cream donut and a pretzel pizza but not the ones you imagined.

@Vivenk88 7 ай бұрын

The first method was good and intuitive.

@UnicornedBatman 7 ай бұрын

I think it would be 65% at the most and 15% at the least

@budsellers 7 ай бұрын

I wasn't sure how to solve it, but it made sense to me to subtract the numbers who didn't eat an item from the 65/100 who ate donuts. Apparently I used method 4. (65-50=15)

@TaIathar 7 ай бұрын

There's an easier way to solve this. Taking Doughnuts as the example, you add up the number of people that did not eat Pretzels (20%), Pizza (20%), or Ice Cream (10%); and then subtract that sum from the total number of people who ate Doughnuts. 20+20+10=50 and 65-50=15 so 15 is the answer. You can technically do this with any of the foods. Taking Pretzels for the next example, 35+20+10=65 and 80-65=15.

@naro1756 4 күн бұрын

I divided it up into 10 sections and marked each one with letters to indicate that the people ate that food.

@mdtalhaansari1096 7 ай бұрын

Solving Geometrically: make a square ABCD of sides 10 each. this represents 100% of visitors. Assign each vertex an food type. lets say A = Donut B = Pretzel C = Pizza D = Ice cream Draw a smaller square from the vertex A of side SQRT(65) Draw a smaller square from the vertex B of side SQRT(80) Draw a smaller square from the vertex C of side SQRT(80) Draw a smaller square from the vertex D of side SQRT(90) The area of rectangle represented by the intersection of all 4 smaller squares is the minimum percentage of people who ate all 4 foods.

@sw413 6 ай бұрын

The title of this video should have been ‘how to over-complicate a easy problem 4 different ways’ 😂

@stevenwilson5556 7 ай бұрын

If we assume that all the non eaters of any category were disjoint (if you don't eat pizza you eat all other 3), then the maximum when you add all up is 10% + 20% + 20% + 35% = 85% meaning at minimum 15% eat all 4, but that could be larger if the don't eat categories are overlapping. If we allow some people to eat none of them, then the max that could eat all 4 would be 65% equal to the smallest category, donuts.

@Barquevious_Jackson 7 ай бұрын

I feel kind of silly now because I just multiplied the percentages of each of the chances assuming it'd show the probability of someone being selected amongst each group (meaning they ate all of the above food items) getting 37.44%. I am not exactly sure why our answers disagree. I think the difference comes down to me assuming that the amount of food purchased would have no correlation to how many more items would be purchased. But because someone would be less likely to buy food after eating it's not sufficient to merely find the chance, you have to find the minimum because you're looking for value already in the data.

@CYXXYC 7 ай бұрын

i did not understand the venn diagram one, but the last minimal proof i understood perfectly lol

@wendellgutierrez761 7 ай бұрын

My line of reasoning was "if I suppose that all of the people who didn't eat an icecream did eat pizza, then that leaves only 70% of the inicial amount as the minimum value for how many ate both", so I could then take those 70% and put it through the same process to find out the least amount of people who would have eaten everything

@x_mau9355 6 ай бұрын

This is very good content

@dminor5085 7 ай бұрын

I used a method similar to the second, take each percentage and minus it from 100 add all the remainders together then take the result away from 100. So it becomes 100-65=35, 100-80=20, 100-80=20, 100-90=10. 35+20+20+10=85. 100-85=15%

@gabesmith9171 7 ай бұрын

I don’t know- but they all busted their New Year’s resolution early this year

@iuer4643 7 ай бұрын

For not "ez" starting percentages, the circles diagram is the best solution

@museofsalzburg2373 7 ай бұрын

I did it by making a rough pie chart of each food's did and did not buy percentages and seeing how you could lay them on top of each other such that the overlap of all 4 takes up the least area, whiich gave way to the delightfully simple solution that the answer is just 100% - the individual percentages of people who did not buy each food.

@naomiparsons462 6 ай бұрын

I remember I got pretty much this exact thing as an extension venn diagram question in year 9. It was from Senior Maths Challenge, I asked the teacher and she looked at it for a bit then gave up.

@earthbind83 7 ай бұрын

Thanks for giving us easy questions sometimes! I used the first method in my head and I feel like I am super smart right now. 🙂 I.e. 65 - 10 - 20 - 20 = 15.

@evilbob840 7 ай бұрын

Same! I started with figuring out 65 - 10 made sense. And then said, "wait, it's as easy as just subtracting the two 20s now."

@Sluppie 7 ай бұрын

So the minimum that bought all four is 15%, the max is 65%, and if all four of these variables are independent then the expected case (0.65 x 0.8 x 0.8 x 0.9) is ~37%.

@Ethan-sc7gq 6 ай бұрын

My guess is 15%. Thinking about it geometrically, you can frame it as an unoptimization problem, where you want as many boxes of a 10x10 grid to be touched by a region of 3 and not 4 foods. Because we are minimizing, there isnt any necessary shape the regions must fill, so we can use that to our advantage. First, choose the 65% as our last food applied. Make a 'layer of the 90% food and 10% from the 65, leaving us with 55. Do this again with the 80%s, keeping in mind that the leftovers from the 80s and the 90 don't have to overlap, so the leftover from the first 80% is 55-20, or 35, then after the next 80%, we have 15. Numerically this looks like[ 65 - (100-90) - (100-80) - (100-80)] %, or 15%. Fun problem :)

@chewy560 6 ай бұрын

Having eaten all for foods I can confirm the ice cream was my favourite.

@HassanAhmed-bs5fn 7 ай бұрын

First: 90% vs 80%, the 10% that didn’t eat from the 90% could of ate part of 80% Thus, there is a minimum of 70% overlap Second: 80% vs 80%, since one of the 80% has a 70% overlap from before, 30% of the people who didn’t overlap could of ate from the other 80% Thus, there is a minimum of 50% overlap Third: 65% vs 80%, since the 80% has a 50% overlap from before, 50% of people who didn’t overlap could of ate from the 65% Thus, there is a minimum of 15% overlap. Didn’t see many people point out the logic, hope this helps.

@WindReader 7 ай бұрын

I can’t believe actually solved one for once. Just subtracted the percentage of each that didn’t eat that thing from 100 and got 15.

@F.E.Terman 7 ай бұрын

Exactly this problem was (in 1885!) subject of Knot X of 'Tangled Tales' by Lewis Carroll. In 'The Chelsea Pensioners', Carroll writes: _Problem_ - If 70 per cent have lost an eye, 75 per cent an ear, 80 per cent an arm, 85 per cent a leg: what percentage, _at least_ , must have lost all four? _Solution_ - (I adopt that of Polar Star, as being better then my own.) Adding the wounds together, we get 70+75+80+85=310, among 100 men; which gives 3 to each, and 4 to 10 men. Therefore the least percentage is 10."

@DanielFSmith 7 ай бұрын

The opening statement is that "the food vendors tell you..." the percentage of foods eaten. But from their perspective, each of the people must buy at least *one* food item (otherwise the vendors would not be able to count the person). So the maximum percentage who eat all four foods should be

@thenonexistinghero 7 ай бұрын

There is no 'lesser than' the maximum. The least eaten food item is eaten by exactly 65% of the people (who buy at least 1 food item). Therefor, the maximum amount of possible people that bought all 4 food items is 65%. It's not at most 65%. It is exactly 65%.

@DanielFSmith 7 ай бұрын

@@thenonexistinghero Show me a solution using the: 20 people example...

@thenonexistinghero 7 ай бұрын

@@DanielFSmith I mean, it's just common sense. Here's a solution with 100 people. 65% of them eat at least 1 food type. So 65 people eat at least 1 food type. It also means 65 people can eat all 4 food types at most. The rest of the percentages don't matter. 65% is the lowest. Whether it's 80% or 90% of people that eat other food types, it's still 65 people at most who can eat all 4 since there's a good chunk of at least 35% that haven't eaten the least popular food and as such, cannot possibly have eaten all types.

@DanielFSmith 7 ай бұрын

@@thenonexistinghero Let's take an example with 60% and, say, 90% using 10 people. Pie. aaaaaa0000 Cake. bbbbbbbb0 Doesn't work... The last person didn't eat at least one. You can only get 50% max.

@thenonexistinghero 7 ай бұрын

@@DanielFSmith They aren't eating from a single slice of pie. The amount of pies is limitless.

@BossitroniuM Ай бұрын

I did the same method as the first one but I only used 10, so I ended with 1.5 people colored in. It was crazy seeing the solution being explained exactly the way I solved it!

@monroeclewis1973 6 ай бұрын

I imagined 100 hungry people. If, for example, 65 ate the first item, 35 did not, and so on for each item. The total of these differences-85- are those who did not eat one item or another. That leaves 15, 100-85 who must have eaten all 4 items.

@randfur 7 ай бұрын

I did the second approach but by combining one extra food item each time.

@TerjeMathisen 5 ай бұрын

This seemed hard for a few seconds until I realized I could invert it. 🙂

@TheDecagn 7 ай бұрын

proud of myself for working this out in my head :)

@chinareds54 7 ай бұрын

The real world conclusion of this story is that the amusement park sells the bundle and finds out that much lower than 15% buy it (probably even less than 5%). The reason being human behavior; no one wants to eat all four at the same time. Even if the bundle were like coupons to be used throughout the day, most people don't plan on eating all four of those items and/or are hesitant to part with their money up front to commit to eating all four. They'd rather just spend their money at POS when they have a craving for something.

@gemstonegynoid7475 7 ай бұрын

Yeah. This is two mains and two desserts. A person might like a deal for one and one. But not all four.

@KroganCharr 7 ай бұрын

The bundles might be interesting for groups that share the food. I don't think it's a very popular idea anyway, though. A third of the people in this scenario apparently just don't like donuts, so they will be skeptical with a bundle that forces them to buy one.

@Farside-mk9ri 7 ай бұрын

Finally. Took me less than a minute to complete. UsuallyI give up. 😅

@alexandros93 7 ай бұрын

Cool problem.❤❤❤

@bledlbledlbledl 7 ай бұрын

what i did was similar to method 1. I imagined 4 rings with gaps in them. a ring 65% complete (with a 35% gap in it), two 80%complete rings, and so on. Turning the rings so that all the gaps lined up, 65% of it was 4 rings thick (that'd be the maximum). Turning the rings so that none of the gaps line up, 15% of it was 4 rings thicc

@fatehero4750 7 ай бұрын

finally a puzzle i solved in seconds

@erikaz1590 7 ай бұрын

"We can imagine Donut-pretzel and pizza slice-ice creams as food." State Fair Vendors: "Hmmmm.."

@diamondore4830 7 ай бұрын

the minimum percentage is 15%, because 35% didn't ate their donuts, 20% pretzels, 20% pizza, and 10% didn't ate their ice cream. While the maximum percentage is simply 65% ate all of their foods, and 10% didn't ate anything

@christinae30 7 ай бұрын

I thought about it for 20 - 30 sec, no calculating (except adding four numbers). Same result as video got. Now I feel intelligent. Nice😉

@plasmaastronaut 7 ай бұрын

that was easy. i found the answer in my head after 30sec thought and i'm average at these puzzles.

@TikiShades 7 ай бұрын

I visualized each being plotted centered in 1/4 of a circle, and seeing how much each overlapped. I realized that there would have to be overlap in every fourth of the circle if you had more than 75%, so i subtracted 75% from the highest value to get 15%. I haven't done much math in a long time but lets see how I did.

@BeefinOut 7 ай бұрын

The real question is, why is everyone eating so much food? The median guest ate at 3 distinct food stands during their trip, that's nuts

@PythonPlusPlus 7 ай бұрын

Given that they could just be getting a drink or a snack, it’s not crazy that they could be visiting 3 food stands in a day at an amusement park.

@gautamsaha9397 6 ай бұрын

Another way to solve. The percentage who didn't take the food is 35+20+20+10=85 So all food are taken by 100-85=15%

@Barteks2x 2 ай бұрын

The way I solved it was sort of a blend of the first and second method (basically the second approach but without thinking about it in terms of venn diagrams, and more like in the first approach instead). I started from the end, figuring out what percentage ate pizza and ice cream: ::::::::.. - pizza (80%) :::::::::. - ice cream (90%) Now the minimum possible overlap looks like this: ::::::::.. - pizza (80%) .::::::::: - ice cream (90%) .:::::::.. - overlap (70%) The I considered "pizza&ice cream" as one food and replaced them in the list with that, with 70% as amount, and repeated that until I was left with all 4 foods as one. So I realized that I only needed to figure out how to solve it for just 2 kinds of foods, and from that I could solve it for any amount. And for just 2 kinds of foods I could easily visualize it (as shown above)

@SytheZN 7 ай бұрын

Why doesn't applying each percentage consecutively work? 90% of 80% of 80% of 65 gives me 37.44% overlap?

@HopUpOutDaBed 7 ай бұрын

That's the equivalent of saying 90% of people who ate ice cream ate pretzels, and 80% of those people ate pizza, etc. Which could be true, if we were looking at probability and the random chances a single person ate all 4 assuming all events are independent the PROBABILITY would be 37.44%. However we aren't looking at random probability a single person ate all 4, we are looking for the minimum number possible which is a completely different question. Just because 90% of the TOTAL # of people ate ice cream doesn't necessarily mean 90% of the people who ate pretzels also ate ice cream.

@fruitshuit 7 ай бұрын

That sort of process works if the four percentages are independent variables! But in this case, the question requires us to assume that the variables are dependent on each other to calculate a worst case scenario.

@octobixer 7 ай бұрын

Unfortunately no as you’re assuming that the portion of people who bought donuts are buying at the exact same ratios as the overall population which my not be true leading to an overestimate

@kenhaley4 3 ай бұрын

Here's how I did it and I think it's simpler than the solution given. Suppose we have 100 visitors. 65 had donuts and 80 had pretzels. That's a total of 145, so we know at least 45 people had both. 80 people had pizza and at least 45 had both pretzels and donuts for a total of 125. So at least 25 people had all three. 90 people had ice cream and at least 25 had the other three for a total of 115, so at least 15 people had all four. Yes, this is pretty close to the Venn diagram solution that Presh gave, but I didn't need a diagram, and quickly arrived at the same answer.

@sunnicivang1093 7 ай бұрын

I was mentally thinking of Method 2, but was physically trying to write it out using Method 1, and using 100 people.

@wombat4693 7 ай бұрын

and here i was trying to figure it out using karnaugh maps lol

@aba_dab_o 7 ай бұрын

Solved it through Method 1. Still trying to wrap my head around the Method 2 venn diagrams, although the Minimal Proof helped it. The Possible trick? is an intriguing and plausible method.

@macdavidson3814 7 ай бұрын

My method was similar to the first one. I thought "What would people have to do in order to get these numbers with the least people getting all 4?" And the answer is everyone who didn't buy 4 is buying 3 items exactly. So I'm assuming that everyone who didn't buy ice cream bought a pizza, a pretzel, and a donut. And everyone who didn't buy a pizza bought icecream, a pretzel and a donut and so on. So I took the inverse of every percentage and added them up since assuming everyone is behaving this way, they are mutually exclusive combinations. They added up to 85%. So 85% of people could buy only 3 items and still get these percentages, so the remaining 15% have to buy all 4.