Could you pass the very first SAT exam? Insanely difficult standardized test

[@verkuilb]

@9:35 Yes, the three you selected are all prime…but an equally valid argument could be made that the other three are all multiples of seven.

[@michaelhallock1428]

That was my immediate answer - multiples 7. I genuinely wonder which answer was intended to be correct.

[@EdwardPerzyk-u9z]

I think the multiples of 7 are MOST CLOSELY RELATED based upon factor of 7, where the prime numbers are only related by being a unique number.

[@maxhagenauer24]

That's why you can't just go by the first pattern you find, there can technically be infinitely many patterns.

[@johnd6980]

I believe that the prime set was the correct answer. It's a more exclusive set than multiples of 7.

[@maxhagenauer24]

@@johnd6980 What do you mean by more exclusive?

[@perakojot6524]

35, 42 and 63 are all divisible by 7, so that's also very probable answer for question of 3 number closely related.

[@mayorb3366]

I also recognized those before I noticed the primes.

[@carlam6669]

35, 42 and 63 are just as related to each other as the other three related numbers because they are all composite numbers.

[@alankilgore1132]

and 35,42,63 are divisible by 3 as well.

[@FoxMcCloudV2]

@@alankilgore1132 Wrong. 35 isn't divisible by 3.

[@akuunreach]

@@alankilgore1132 Please divide 35 by 3 It happens to us all from time to time, so don't feel bad 😄

[@cristinacu2286]

10:55 im thinking Romania Bulgaria and Greece, balkan countries?

[@oliviervancantfort5327]

Yes, Romania and Greece border Bulgaria

[@CatholicSatan]

Definitely not Norwary...!

[@tselkovyy]

I thought about this but here what i've found out Norway, Denmark and greece have cross on their flags norway, greace and romania have blue colour on the flags bulgaria japan and romania were in axis but it's 1926 test so their capitals starts with consonants norway denmark and japan had kings (and stil has) but the only thing i'm interested is why it's written Norwary and Roumania

[@rlkinnard]

my thought, too.

[@ProjectGeekPL]

​@@tselkovyythere are only 3 countries spelled. Correctly 😮

[@redgribben7679]

Denmark, Norway, Bulgaria, Romania, Greece and Japan could be much more difficult than it looks on the surface. The most obvious answer today would be that Bulgaria, Romania and Greece are all part of the Balkans, and that they all three follow orthodox christianity. Now a different connection could also be Romania, Greece and Japan as they were all members of the Entente during WW1 and they all gained territory through the peace treaties with the age of the exam this is an actual plausible connection, as i would assume it would be common knowledge of who fought on the same side as the US during the Great War in 1926. Further connections could be Denmark, Norway and Romania as they all use modified Latin alphabets or even the reverse Greece, Bulgaria and Japan none of them use the Latin alphabet.

[@damienknight5655]

Considering most closely related, I think the most obvious answer should probably be the right one.. That they are all Balkan countries or at least eastern European countries

[@redgribben7679]

@@joakimforslund3609 Neither Denmark nor Greece are exclusively island nations. Denmark and Greece has a lot of Islands, but more than half the total area of Denmark is an peninsula. I would imagine the same is the case for Greece that most of the country is attached to continental Europe.

[@SR-ml4dn]

@@joakimforslund3609 Denmark is not an Island , Jutland is part of Denmark and is a peninsula connected to germany. Greece by they way is not a Island either. When did you last look at a map ?

[@chrisb8698]

4:30 I love how this question appears straight forward, but it can actually be slightly nuanced. Reminiscent of the classic "frog climbing out of a well" type question, the man will actually hit $300 before the 50th week. He'll reach $302 on the 48th week upon obtaining his salary, but will of course spend back under. This nuance could be addressed by a simple adjustment to the wording of the question, e.g. "How many weeks would it take for the man to end the week with $300?"

[@Tahgtahv]

I think the key word here is "save". I agree if it was replaced with a more generic term, eg "have $300" that it would be unclear like you say.

[@TheEvinB]

The way you've worded the question I would say is more ambiguous. The word "save" is pretty clear in its meaning (to me), in that it's not money you have only obtained but instead money you have deliberately put aside for a later date. So until the money is put in his piggy bank it's not considered saved.

[@acmhfmggru]

He gets his salary and pays his debts at the same time.

[@alanmon2690]

Nominative is the subject, accusative is the direct object, dative is the indirect - -terms that are essential when learning Gerrman. There's also genitive.

[@GodmanchesterGoblin]

Also pretty much anyone who studied Latin would know all of these - Nominative, Vocative, Accusative, Genative, Dative, Ablative.

[@chrishogan6273]

Den fisch isst das Mädchen

[@thisnthat3530]

@@chrishogan6273 Not to be confused with "Der fisch isst das Mädchen"

[@yurenchu]

​@@chrishogan6273 _Fisch_ is a German noun and hence is always spelled with a capital letter F.

[@michaelblankenau6598]

Trump said there are only 2 genitives.

[@wolfganghermesmeier]

Norway, Denmark and Greece are on peninsulas, but maybe this is better: Bulgaria, Roumania and Greece are neighbouring countries.

[@chongli297]

I don't think there is such an issue with having "only 20 seconds" for these. Many of the questions you can do in 3-4 seconds, allowing you to save up a lot of time for the harder ones (such as the number sequences)

[@GodmanchesterGoblin]

Exactly my take. The earlier questions that Presh covered were very straightforward.

[@richardwhite2304]

Looks like Mavis, Djer Kiss and Jonteel were all cosmetic companies in 1926

[@Toshinben]

You serious!? That'd make the question heavily biased toward girls; they'd be more likely to shop for these products and have learned major brand names.

[@travisterry2200]

I think the other names were other random store products. Del Monte is still canned fruit I believe.

[@celia222]

Bon Ton and Gossard are lingerie brands. I think they are still around?

[@jamesschaaf612]

@@celia222 Bon Ton in 1926 actually seems to have sold candy.

[@richardwhite2304]

@@Toshinben or more likely accessible to all kids with stay at home moms with disposable income

[@RabblesTheBinx]

19:45 of course not. A wizard's primary stat is INT, not WIS.

[@verkuilb]

For some wizards, the primary stat is quidditch goals scored.

[@RabblesTheBinx]

@verkuilb oh, don't get me started on all the reasons those "wizards" are really sorcerers.

[@fare-5174]

It's mind-boggling those are all 20-second questions. It implies you do not have the time to write anything down and have to deduct the answer immediately, without any intermediate steps. Some word games might be good enough for that kind of pace, but the rest is brutal. Did the test have any kind of preparatory courses beforehand? I frankly do not see many students passing the exam without extensive couching a century ago (and frankly, even today).

[@howareyou4400]

yeah, 20 seconds means it's only for simple questions. Any difficult question is not solvable unless the students have practiced it before (and practiced not only how to solve it but also repeatedly so they can do the calculations fast. they do not have a calculator back then). These are pretty much the opposite of what education should encourage.

[@GodmanchesterGoblin]

Many of the early questions were trivial, taking only 2 or 3 seconds to identify the correct result. I was genuinely surprised that Presh did not know some of them. But then I was at school in the UK in the 60s and 70s, may be things have changed since then. The diminishing powers with alternating signs would have stumped me too, though.

[@verkuilb]

Not all questions are “20 seconds”-test takers just need to AVERAGE 20 seconds per question IF they are to answer all the questions. Many test takers (then and now) do not finish.

[@jeepien]

Presuming there are many questions that can be answered in under five seconds, that leaves a lot of extra time for the more difficult problems. Presuming all questions count equally, the best strategy would be to solve the most obvious first, then go back for those that take more analylsys to solve

[@svans6725]

14:43 I have just noticed that you can calculate squares by adding consecutive odd numbers to the previous square. 1^2+3=4 2^2+5=9 3^2+7=16 4^2+9=25 X^2 +2x+1= (X+1)^2

[@asdfsdfghjkjkl]

well, if you take the previous square (say it's a 2x2), and you want to extend it to a 3x3, you can extend it once downward (making a 2x3), then extending it once rightward (making a 3x3). this adds the side length of the current square, and the side length of the current square + 1

[@rdfodra]

And the sum of the first n odd numbers is n squared.

[@asdfsdfghjkjkl]

@ yep it's clear from a grid where you color every other layer; then count the amount of new squares that appear (1, 3, 5, 7, 9, etc, etc.)

[@Angi_Mathochist]

Yes, that is well known. I noticed the numbers were adding consecutive odds without actually noticing that they were squares. :) I was just looking for the pattern to get the answer quickly -- I wasn't paying a much attention to what they WERE. :)

[@verkuilb]

@@asdfsdfghjkjkl Exactly. Similarly, if you take that same idea into 3 dimensions, it becomes clear that the difference between n^3 and (n+1)^3 is 3n^2 + 3n + 1.

[@eddyjowhitley4309]

9:36 I saw the other three numbers in the group being related before I saw the prime numbers. 35, 42, and 63 are all multiples of 7.

[@thomashoffmann8857]

They are all 0 mod 7. They belong to the same equivalence class

[@acmhfmggru]

it asks for the best answer, not the second best answer :)

[@eddyjowhitley4309]

@@acmhfmggru "Best" is subjective in this case, as the answer key is lost. Subjectively, I felt as though the best answer was my above comment. We don't know what the best answer really is. EDIT: subjectivity is not the word I was looking for here. And your statement can still be correct

[@acmhfmggru]

@@eddyjowhitley4309 Primality is objectively more important and rare than equivalency under mod 7. Your feelings don't enter the discussion, this is math, kid.

[@eddyjowhitley4309]

​​​@@acmhfmggru ok, let's get objective then. Reading the directions of the problem, it states to choose which words, or in this case numbers, that are most closely related. Per Google, related numbers are a "set of numbers that are connected through a mathematical relationship, often involving the same digits used in different operations like addition and subtraction, or multiplication and division." Operations. Like dividing. Hence, 35, 42, and 63 are all related numbers because they share a common divisor of 7. That said, the definition says prime numbers are also mathematically related because they are the building blocks of divisibility. I see the argument used for having the prime numbers be the correct cluster, but the directions are rather vague. Objectively, because the key is lost, there is no "correct" answer, so we are only left to our devices to decide that for ourselves. And based on this discussion, it appears as though not all of us think the same about which relationship the question was looking for. Until the key resurfaces, no one will know truly what the answer is. Even Presh himself said he "thinks" that the prime cluster is correct. It is merely supposition.

[@ElderEagle42]

10:49 I believe the answer to be Bulgaria, Greece and Roumania, since they are all in the Balkans

[@activeentropy]

Not just that but they share borders.

[@RabblesTheBinx]

Oh, yeah, that makes more sense than my hypotheses. I was thinking it was either Bulgaria/Denmark/Greece because they're European countries that actually exist (Japan is in Asia, and there are no countries called Norwary or Roumania). My other thought was _Norway,_ Denmark, and _Romania,_ because they all use the Latin alphabet (though, fun fact, Romania _used_ to use Cyrillic, despite being a Romance language), but the other three countries don't. But, yeah, Bulgaria, Romania, and Greece all being in the Balkans and sharing some borders is definitely more logical. But if I got that question on the SAT, I would still have gone with my first answer and argued with the proctor when I got marked wrong. Cuz, come on, man, you can't have typos like that on a _test!_

[@malavkunj3951]

Also norway denmark and greece have a cross on their flag

[@BaranCemCesme]

But is it spelled "Roumania"

[@XiuHang]

The question at 9:35 is pretty gross. Yes Primes work. As another commenter pointed out the others are multiples of 7. I probably would have answered 42, 47, 53 because they are literally the closest to each other, as in the difference between those numbers are the smallest. I'd also argue that you could make a case for 35, 53, 63 because they all have the digit 3.

[@acmhfmggru]

It is pretty clear about picking the "best" answer. Those are all answers, but they aren't the best answer. You can always make a case for picking the first 3 on the left because they are the leftmost.

[@XiuHang]

So then which answer is the "best" answer to the specific phrasing of the question? My point was that the "best" answer is ambiguous. My proposed answer uses the most literal interpretation of the question. Does that make it the best? What's better? Sharing a factor or falling under an arbitrary grouping? Hypothetically if the six things were: Corolla, Accord, Tacoma, F-150, RAV4, Gladiator What would be the better answer here? Is it the Toyota's or the pickup trucks, and why is one grouping better than the other?

[@Skank_and_Gutterboy]

@@XiuHang I agree, "best" is in the opinion of the test writer. This test is deeply flawed, what good are these number theory questions? When I took the SAT in the 1980s, it didn't have number theory questions, which I agree with. People go into this area of study because they find it interesting. For the other 99.999% of us, it's worthless.

[@acmhfmggru]

@ no, there's no ambiguity. The best answer is the one with the least number of assumptions and choices built into it. Your division class modulo 7 answer has two basic arbitrary choices baked into it: use modulo 7 arithmetic, look at equivalency class [[0]]. The primality answer is better because it has no baked in assumptions. This is the essence of the question. It isn't that there is more than one BEST answer, it is that there are multiple valid answers and you are tasked with picking the BEST answer. Just take the L and move on with your life.

[@XiuHang]

@ You're the one who added the "two basic arbitrary choices." to the multiples of 7. The point is simple, there is nothing that makes prime numbers MORE OR LESS closely related than any other category of numbers. In this case, multiples of 7. You also appear to have not read my original comment where I supposed my answer as something completely different, but that's okay. You can say "The best answer is the one with the least number of assumptions and choices built into it." but my point was no matter what grouping you decide to go with it will work on some level of assumption. The funny thing here is that we don't even know what the "correct" answer is. The answer key was lost. You're the one assuming your answer is the correct one. Ironically enough, by your standard my answer would be better than yours because my answer was the one that took the question most literally. I won't respond to anything after this because it is entirely pointless, but I would suggest you look into the basic concept of intellectual humility. You assumed a correct answer then defined another equally correct answer as wrong because of your arbitrary redefining of the answer to make it less direct.

[@verkuilb]

@8:54 You got the answer right, but opened your answer by saying “the first four items are fruits”. Actually, the fifth item-a prune-is also a fruit.

[@michaelhallock1428]

Dried plum to be precise.

[@azrobbins01]

Kinda, but there is no fruit called prunes. It would be like saying a raisin is a fruit, or a pickle is a vegetable. It is the product of a fruit or vegetable, but not in its pure form.

[@verkuilb]

@@azrobbins01 A raisin IS a fruit. A pickle IS a vegetable. Drying a fruit does not remove it from the fruit category . Pickling a vegetable does not remove it from the vegetable category.

[@azrobbins01]

@@verkuilb I disagree. A cucumber is a vegetable. A pickle and a cucumber are not the same thing. A plum is a fruit. A prune and a plum are not the same thing.

[@michaelblankenau6598]

But we don’t generally classify raisins as fruits either even though they are dried grapes.

[@MegaSuperEnrique]

The lost language section sounds like someone was promoting Esperanto

[@mladend]

If a clock gains 36 minutes in 30 hours, it will gain 36 seconds in 30 minutes (half an hour). I would say it's a trick question. :)

[@ianmalcolm2552]

I don’t think it’s a trick question, I do think Presh over complicated how to calculate the answer though.

[@mihailghinea]

Yeah, its 36/30×60/2 I think he overcomplicated his answer :)

[@GodmanchesterGoblin]

How I approached it.. 36 minutes in 30 hours, is 36 minutes in 60 half hours. So in one half hour it gains 36 minutes divided by 60. 36 minutes divided by 6 is 6 minutes. 6 minutes is 360 seconds, and divided by 10 gives 36 seconds as the answer. It took barely 5 seconds to work out and a minute to type...

[@RabblesTheBinx]

I mean, technically speaking, Presh just did exactly the same process you did, just in a way that's more acceptable in a mathematics class. Your whole mental process there was literally just a shortcut to do the exact same math. As far as why it's important, well... How much time does the watch gain in 42 minutes?

[@GodmanchesterGoblin]

@@RabblesTheBinx That's a good point, thanks.

[@humptwe]

10:49 I believe answer to be Norway, Denmark, and Greece because each country has a plus shape on their flag, even in 1926 when this test was given

[@RabblesTheBinx]

Wow, I'm starting to see there are a lot of potential logical answers... But almost all of them only work if you accept that Norwary and Roumania are typos and not intentional misspellings... Yeah, I'm going back to my original answer, Bulgaria/Denmark/Greece, the only European countries listed because Roumania and Norwary are not real places.

[@futurepath]

I really enjoyed this video and the comments! Great video of the old SAT

[@aba_dab_o]

Thanks for the video! As an infrequent scorer of math standardized tests, it was quite interesting to see what the SAT was when it first started compared to now. In any regard they had to start somewhere; then potentially change & improve it in following years. 🙂

[@ericherde1]

2:34 There is no reason for anyone who only speaks English to know this. That’s the sort of question that should be on a German or Latin grammar test, not an English one.

[@yurenchu]

Not everybody needs to know about accusative (or dative, verb, adjective, or protoplasm). But also, not everybody needs to go to college.

[@ericherde1]

Verbs and adjectives are English grammar. Protoplasm is biology knowledge that is generally expected common knowledge among aducated people. Grammatical structure of certain foreign languages are not generally expected common knowledge among educated people. Sure, most colleges expect their students to have some foreign language knowledge, but someone could be highly educated in English and fluent in Spanish without knowing anything about noun cases. There might as well be a question asking about the different tones in Mandarin, or the different clicks that are used in certain languages indigenous to southern Africa. Those are things that are important to know if you want to understand those specific languages, but completely unnecessary (and unreasonable to expect) for an American whose only foreign language experience is with languages that don’t have those features.

[@geraldcollins5684]

I got this one easily enough. ANd I'm in the US and only speak English. It's just a matter of having a good vocabulary to begin with so you can eliminate the obvious wrong and see what was left. TBH, there wasn't anything else left when I went through the list.

[@yurenchu]

@@ericherde1 The English language _does_ have the accusative (a.k.a. direct object) and the dative (a.k.a. indirect object), just as the English language has so-called _second person singular_ verb and _first person plural_ verb, even though the forms of those two verbs are generally identical. My guess is that educated Spanish people (or educated people whose native language is Spanish) would also know about _acusativo_ ( _objeto directo_ ) and _dativo_ ( _objeto indirecto_ ), even though most forms of those cases in the Spanish language may be identical. It's about knowledge of grammar structures of your own language. Educated people in North America most likely also know about kangaroos, wombats, platypuses and cassowaries occurring in Australia/Oceania, even though those people will never have to deal with such animals (unless perhaps when they work at a zoo; but not everybody has to work at a zoo, so not everybody needs to know about these animals).

[@ericherde1]

@@yurenchu You might as well say that English has the subjunctive mood, since we have one verb that differs in form between indicative and subjunctive uses. The only words in English or Spanish that actually have any case differences between accusative and dative on the one hand and subject positions on the other are pronouns. And those are generally referred to just as subject pronouns and object pronouns. One might learn the case words for the concepts in an advanced class in college, but there is no reason to expect someone to already know them in a college entrance exam like the SAT. Should the test also be asking about derivatives and integrals? After all, lots of well-educated people know calculus, even though most people haven't studied it yet when entering college.

[@JoeHarpo]

At around 9:42 you correctly point out that 79, 47 & 53 are prime, however, it's arguable that the correct answer is the other 3 numbers, 35, 42 & 63 because they're all divisible by 7.

[@kenhaley4]

AI came up with the following for the words at 10:30: The words you provided, Bon Ton, Gossard, Djer Kiss, Del Monte, Mavis, and Jonteel, were all popular brand names in the 1920s. Bon Ton was a popular department store chain. Gossard was a well-known lingerie brand. Djer Kiss was a famous perfume. Del Monte was a leading food processing company. Mavis was a popular brand of hair care products. Jonteel was another perfume brand. This would still be tough to identify the 3 most closely related. I would probably guess Djer Kiss, Mavis, and Jonteel, as they are products applied to the body, as opposed to clothing.

[@rjohnson8ball]

A cornet is a brass instrument which I would not describe as small. A flute is a small wind instrument with valves used to alter the column of air flow and vibration.

[@gcewing]

Google says a cornet is 13 to 16 inches long, and a standard flute is about 26 inches long.

[@acaryadasa]

But a flute has no "auxillary bands of tubing". It just has the single tube, whereas a cornet does.

[@jeepien]

But a flute does not work by changing to the total length of the path.

[@mstmar]

@15:39, i noticed that all the numbers are squares +3, in particular, the squares of triangle numbers. 3=0^2+3, 4 = 1^2+3, 12=3^2+3, 39 = 6^2+3, 103=10^2+3. so the following numbers would be 15^2+3=228 and 21^2+3=444. neat how there are 2 ways to get the same values

[@tinnguyen5055]

This is how I solved it aswell 😂

[@kozatas]

10 is not a triangle number?

[@tinnguyen5055]

@kozatas these are not triangle numbers. The sequence 0 1 3 6 10, has the difference of consecutive numbers of 1 2 3 4, so to get the next u add 5 to get 15, then add 6 to get 21

[@mstmar]

@@kozatas a triangle number is a number that is the sum of the first n numbers for an integer n. 10 = 1+2+3+4 so it's a triangle number (with n = 4).

[@azrobbins01]

At 9:44, you said the 3 numbers were related because they were all primes, but I would have chosen the other three since they are non-primes. Does that make my answer wrong? Isn't that the same thing?

[@davidlindstrom4383]

Not only are the other 3 non-primes, they are also all multiples of 7. I argue this makes them more related than the 3 prime numbers.

[@joshuawood-bz9gu]

the question asks for what are most closely related. Things are more closely related for what they are, than what they aren't. for instance, water, ICBMs, and bullfrogs are all not John Cena, but that doesn't make them closely related

[@azrobbins01]

@@joshuawood-bz9gu That makes sense.

[@yurenchu]

​@@joshuawood-bz9gu Yes, and the multiples of 7 _are_ multiples of 7 , while these primes _are not_ multiples of 7 . In fact, the definition of prime numbers basically comes down to that they are not related to each other at all! If you had to choose _four_ numbers that are most closely related out of the following _seven_ numbers: 79 , 35 , 47 , 42 , 53 , 63 , 7 would you have chosen the four multiples of 7 , or the four primes? I think that 7 is more closely related to 35 , 42 and 63 than to 47 , 53 and 79 .

[@geraldcollins5684]

@@yurenchu But two of the muitipliers were odd and one was even so less related. I saw both solutions, but settled on the prim answer.

[@nicholasharvey1232]

15:27 I arrived at the same answers by subtracting 3 from each number to create the sequence 0, 1, 9, 36, 100. The square roots of these numbers are 0, 1, 3, 6, and 10 (the so-called "triangle numbers"). The next two triangle numbers are 15 and 21, so I just squared those and added 3 to get 228 and 444.

[@kenhaley4]

Some of the questions refer to contemporary knowledge or common vocabulary which has changed considerably in the last 120 years. For example, at 10:30, these names might refer to common brand names of products of the day or something. Same for the grammar questions: I don't think we refer to the "accusative case" today.

[@KateGladstone]

Yes, we still refer to the accusative case: Google it or search it on Wikipedia.

[@Token_Civilian]

Two quibbles - At 9:42 where you said 3 prime numbers. The other 3 numbers are all simple multiples of 7, which are IMO an equally valid choice. At 11:09 - the three are Bulgaria, Greece, Romania, all SE European nation states.

[@mandolinic]

English doesn't really have cases (where the word ending changes to indicate grammatical use) , but I guess many students at that time would have learned Latin (which most definitely does have cases). With Latin, the accusative case is used to show the direct object. Amongst others, Latin also has the dative case, which is used for indirect objects, and the nominative case for the person, etc, who is doing that action. For example: The teacher (nominative case) gave the book (accusative case) to the student (dative case). Be careful, Latin is a very deep rabbit hole, and if you fall down it, then it's really easy to fall under its spell.

[@yurenchu]

English pronouns do have cases, although there is no distinction between dative and accusative (e.g. _I_ / _me_ , _he_ / _him_ , _she_ / _her_ , _we_ / _us_ , _they_ / _them_ ; and also _thou_ / _thee_ ).

[@mandolinic]

@@yurenchu Excellent point. No dative, but definitely genitive forms (e.g my pen, his book, your house, its shell, etc). I assume these are all hangovers from the time when English did have cases.

[@yurenchu]

@@mandolinic Thanks for your reply. Words like _my_ , _your_ , _its_ , _our_ , _their_ are not genitive case pronouns, they are possessive determiners. I think the English genitive case pronouns are _mine_ , _yours_ , _hers_ , _ours_ , _theirs_ (and _thine_ ), but I'm not sure about that.

[@MrMayhem010]

Some of these questions were interesting, and I wish that they were used on today's SAT

[@joe_z]

4:17 I guessed flute because I've never heard of a cornet, but I guess a flute doesn't have any "auxiliary bands"?

[@oldguy-hz4jd4go1i]

A cornet is closely related to a trumpet. The key is that it has pistons and valves.

[@kindreon]

@22:02 seems to be incorrect. I think the premise of "people's tastes vary" means there's independence. Thus the situation is memoryless like asking if you've flipped a coin 10 times and got 10 heads whether the next flip is more likely to be heads or tails. It's undetermined. To me, it's different from @21:03 since lecture quality isn't independent of the professor who gives the lecture since there's a causal relation between presenter and presentation quality. Well, this might not be true in a few decades with AI-augmented presentations, but I'm pretty sure they didn't have ChatGPT back in 1926.

[@verkuilb]

No. The “tastes vary” statement is simply emphasizing that the answer is NOT “necessarily true”. However, 15 out of 15 is a significant enough sample to indicate that this is not just a coin flip, and that the artwork has appeal which is substantially greater than 50/50.

[@kindreon]

@@verkuilb The instructions say to take the premise as given not extrapolate to only an implication on certainty. To me, "people's tastes vary" should be interpreted literally as "what appeals to each person is different." If so, it doesn't matter if the artwork already appealed to the entire planet except 1 person, that last person's taste may vary, ie: is undetermined. Conversely, you'd need to stretch the meaning of "people's tastes vary" for it to stay true if your sampling argument holds. Based on your phrasing, you seem to subtly assume appeal is a property of the artwork, which I think is a mistake. Also, the coin analogy was for highlighting independence not that coins normally have fair bias.

[@verkuilb]

⁠@@kindreon It’s not a mistake. Here’s a different wording of a similar problem: a 20-sided die has every side painted either green or red, but you don’t know how many sides are each color, and in fact you don’t know if both colors even appear. 15 people roll the die, and all 15 roll green. “The sixteenth person will roll green.” Necessarily true, necessarily false, probable true, probably false, or undetermined? Your logic would conclude that it’s undetermined-but that is clearly wrong. The fact that 15 out of 15 people rolled green indicates that the die is almost definitely well over half green, and that makes the statement “probably true”. The 15 out of 15 green rollers statistically demonstrates the high likelihood that overwhelming greenness of the die is a property of the die, just as the 15 out of 15 people liking the art demonstrates that the overwhelming appeal of the artwork is a property of the artwork.

[@kindreon]

@@verkuilb Except with the artwork you're rolling 15 different dice. To me, appeal is more sensibly something the viewer experiences. The artwork dictates nothing about each viewer's appeal function. There being multiple dice is what separates this problem from the lecture one due to the "people's tastes vary" premise. Looking back, my attempt to highlight independence with the coin flipping example was confusing, so just ignore it if it helps. I think our disagreement boils down to if you should assume a person's appeal function is an independent dice roll, ie: how "taste" works. If not, your sampling argument would be correct, but I think people generally don't think of "taste" this way. As such, no sample of other people's rolls tells you anything about how someone's dice is weighted and the answer should be undetermined.

[@petersage5157]

"There's this whole trick for antonyms, but...uh, this isn't the place."

[@ZijZijnZijnZoons]

I think the question listing six different countries where you have to find the three closely related is a bit of a challenge, because it's conceivable the answer in 1926 could be much different than it is in 2025.

[@roginutah]

Current map indicates Romania, Bulgaria and Greece are all adjacent

[@murtadah6327]

I enjoyed watching the video and tried to participate solving the questions from various sections challenging numerous mental faculties. I can say, It was moderately tough for me.

[@angrytedtalks]

Holy moly. Those brand names are a puzzle.

[@Duck_Bidiyani]

3:45 I have played the French Horn for 4 years now. From what I know, "Unison" refers to people playing notes with a 1 - 1 ratio in vibration frequency while octave refers to the interval between where the notes repeat. So I think octave is the correct answer for that one

[@LanceRyley]

As an interesting side note, the military uses a variation on the artificial language test to determine if you have an aptitude for learning foreign languages. It's called the Defense Language Aptitude Battery, it's a timed test, and it basically builds vocabulary and grammar for a made up language and you have to decide which sentence is correct. I took in in '87 so I don't know if they still use it, but my results were good enough for them to send me to DLI in California for a couple years to learn Czech.

[@robheale9860]

This is different. A Mind Your Decisions video where the questions are not all mathematical or logical.

[@normalchannel2185]

9:35 OBJECTION! The other 3 numbers 35, 42 and 63 are also as related to each other as 79, 47 and 53 are. 79-47-53 are all primes, and 35-42-63 are all composite numbers. The number of composite and prime numbers is equal, since both are infinite. Plus the first set is also all divisible by 7

[@soundsoflife9549]

I chose the multiple of 7 also.

@10:42 Bulgaria, Greece and Romania have territories in the Balkan Peninsula.

[@dhpbear2]

1:46 - First one is made easier by the 'an'; only the words that start with a *vowel* need to be examined!

[@MrBradleykeith]

These are the sort of questions that lead to critical thinking and understanding. I got 95% correct, but took a little too long to answer some of them.( OK I'm 67 and my ability to read is a little slower now) 😀

[@boycetowell4463]

Greece, Bulgaria, and Romania are related in that they are contiguous countries. Greece borders Bulgaria, and Bulgaria borders Romania

[@thomashoffmann8857]

All are in eastern Europe

[@ProjectGeekPL]

Norway Denmark and Greece have cross in their flags

[@mayorb3366]

Same type thing- I found my grandmother's Regents Exams question books from high school, 1917. A lot of the questions would be archaic today (reckoning), and many of the grammar questions would stump people with English degrees today.

[@empmachine]

This is one of your best recent videos!! I can't believe how much my grammar knowledge slipped.. (I'm gonna have to side-quest that for a bit!) The idea of covering more general knowledge is a good line IMHO (you can just add it on top of your amazing puzzles) MORE PLEASE!!

[@blacklion79]

I like these. Artificial languge part is like modern Linguistic Olympics questions at city-level of competition hierarchy. Many other sections could be ib pipular quiz shows or bar quizzes nowadays.

[@jgfaustus]

10:23 Bon Ton, etc. are/were brands. Bon Ton is/was a chain of department stores, Gossard is lingerie, Jonteel cosmetics, Del Monte canned fruit, Mavis apparently perfume, Djer Kiss cosmetics. So I guess the two cosmetic brands plus the perfume make the most related ones.

[@craigmooring2091]

Regarding the 3 related example that starts with Norway, I selected Bulgaria, Romania, and Greece as being contiguous and all being bordered by inland seas not regarded as parts of an ocean. In fact, in the not terribly distant past, when sea level was considerably lower due to glaciation, Gibraltar was connected to Africa and the Mediterranean was mostly dry land. Bon Ton. like the other 5 in the line, is a Brand Name. The 3 I would think most closely related are Gossard, a maker of ladies' undergarments, Djer Kiss, a maker of upscale compacts, and Jonteel famous for its indelible lipstick.

[@Chaosbringer77]

Did any student actually finish the entire test making good time use??

[@castleanthrax1833]

Possibly. I'd skip questions that the answers weren't immediately apparent and then go back at the end, so I'm sure a very small group of very intelligent children got them all answered (I'm not implying I'd be in that group, but I'd like to think I'd be close).

[@boysen01]

As for the countries at 10:55, Greece, Bulgaria and Romania are all connected through their borders. Greece to Bulgaria, Bulgaria to Romania

[@ericshelby8813]

I'm glad they got rid of the Analogies portion of the SAT. I was never good at them. When I used SAT preparation materials, I asked my dad who is as smart as I am to help me with the Analogies problems, but even he couldn't figure them out. I suppose it's to test your analytical capability, but when you have only about 20 seconds to solve a question, you likely wouldn't be able to analyze the question in time.

[@andresfriant-hm2ot]

4:50 I'm pretty sure the idea was the same that you explained in the "Internet shocked by teacher's mistake" video, like, off-by-one error but I'm not sure now because it does say save and not reach. It could be in the 48th week because it reaches $302 but during the week he will spend it so he is not saving it. If I'm right or wrong let me know.

[@Angi_Mathochist]

I'm sad they got rid of the analogies! That was the most recognizable, iconic part of the SAT. That's arguably what MADE it the SAT, for so long. And I was good at them, too. Why did they take them out?

[@blobfish1112]

14:42 Also differences between numbers are 11, 13, 15, 17, 19, 21.

[@rishabhghughal5688]

For the analogies, I could be wrong but I believe that on the "beacon : helmsman" one, the answer was actually "wisdom : wizard". If you analyze the prefix and suffix of wizard, it literally translates to "wiz"(wisdom)-"ard"(one who holds to a great excess). A helmsman holds a beacon to excess, and a Wizard holds wisdom to excess. I don't think that in the 1920's people had the same idea of wizards as we did today, probably changed by Harry Potter, Lord of the Rings and other fantasies

[@happyhippo4664]

I would have done very well but not perfect. I took the SAT in 1977. I don't remember my score but I remember getting in the 99 percentile in math and in the 80s percentiles in the other categories. I ended up being a chemical engineer. I had a very good vocabulary because I took Latin and a vocabulary course in high school. Even then, in some of those analogy questions, I didn't know a lot of meanings.

[@howareyou4400]

I heard that the difficulty of SAT goes to peak around 70s and 80s, then go down after 90s. Nowadays it's extremely easy such that top elementary school students can often get really good score.

[@happyhippo4664]

@howareyou4400 my son graduated in 2012. He didn't even take the SAT. Everyone seemed to be taking the ACT.

[@TheDarkEnforcer]

@MindYourDecisions Error in video at 25:32: You said "word" but the screen shows the word "work".

[@hajinezhad3]

Bon Ton, Gossard, Djer Kiss, Del Monte, Mavis, Jonteel You could say three of the words contain the the word "on" within them or have anagrams of "ton" (Bon Ton, Del Monte, Jonteel). You could also say three of the words are one-word and three are two-word combinations, but in that case you couldn't differentiate between the two, so that would not be a way to group them.

[@pi-sx3mb]

I just took the SAT. The first question right out of the gate was a ball-buster: "What is your favorite color?" I got it wrong, but fortunately they graded the exam on the curve so I got a score of 1600. As Mona Lisa Vito so astutely observed, "It's a trick question Your Honor".

[@philliberatore4265]

"What is your favorite color?" "Blue ... no" Ahhhhgggg

[@pi-sx3mb]

@@philliberatore4265 LOL, fortunately the math section did not ask anything about speed velocities. 😊

[@ange_does_gacha_art6640]

Wait, why would they ask a person's favourite colour on the SAT??

[@pi-sx3mb]

@@ange_does_gacha_art6640 To separate the genuises from the dummies. Anyone with a brain knows the correct answer is green. I mean purple. Or it could be periwinkle, although that's more of a shade than a color I suppose... 👀

[@yurenchu]

@@ange_does_gacha_art6640 Test taker: "Chartreuse." Examinators: "Welcome to Club Elite."

[@mrsergio5658]

first number series could also fit 37 and 48: ignoring the initial numbers (which we can assume are "given"), starting from 7 you have [(N + next) - previous], where next and previous are the numbers that come after and before the current N. So: 7 + 18 - 4 = 21 18 + 21 - 7 = 32 21 + 32 - 18 = 37 32 + 37 - 21 = 48 I know I'm assuming, but this kind of puzzles usually give you the first three numbers by default, otherwise you can't find any rule at all, so I believe my solution is also valid :)

[@yurenchu]

"21 + 32 - 18 = 37" That doesn't appear to be correct.

[@raendom179]

At 7:51 , shouldn't the answer be 24 feet, since the rear wheel makes two complete revolution for each revolution the gear wheel makes?

[@Khantia]

10:45 as someone living in Europe, I'd say that Bulgaria, Greece and Romania are most closely related, as they are neighboring countries (Bulgaria is sandwiched between the other 2), and somewhat culturally similar.

[@josephfredbill]

Prime numbers - yeah, but the other three are all multiples of 7 so - you make your choice - are prime numbers more closely related than muliples of 7? Opinions may differ

[@dhwyll]

21:04 I'm surprised a mathematician would say "Probably True." Each lecture is independent and this past performance is no indication of future performance. "Undetermined."

[@nitinjaganath1004]

That's not correct. Let's take another example. There is an actor whose previous movies were all good. You would go to watch his future movies in theatre because there is a high probability that this will also be good. Looking at every outcome as independent, is not correct. An actor is presumed to be good because his acting is good, you can't expect his acting to degrade all of a sudden in his next movie. Indeterminate is only if we have exactly 50% chance. Even if we have 55% we can say probably true

[@dhwyll]

@nitinjaganath1004 That presumes past actions are indicative of future actions. That isn't true in this case. Indeed, if we could ascribe a probability to the lecture, we could distinguish between Necessarily and Probably, but we can't. It's akin to the question of if you have a coin that lands heads 15 times in a row, what's the likelihood of it landing heads on the 16th toss...and insisting that the coin isn't fair but is instead a double-headed coin. That's a possibility, but we have no reason to declare that to be true or even "probably" true. Such outcomes, while rare, are possible. We have no justification to think the coin is rigged as opposed to fair. And same here. There is no reason to think the next performance will be connected to the previous ones.

[@roginutah]

Instructions read: "premise is true and unquestioned" So Prof Johnson: Necessarily true, since "ALL" lectures were interesting.

[@dhwyll]

@roginutah Nobody is denying that every previous lecture was interesting. There is no information as to *WHY* they were. The lectures given *WERE* interesting. We have no information about future lectures. Thus, we cannot assume that past performance is indicative of future results. Undetermined.

[@apinkpaintbucket]

​@dhwyll I'm confused by what you were trying to convey with your coin example. The way I see it, your coin example is a perfect explanation for why Probably True is the right answer. It's true that every lecture is independent and random, but random variables still have probabilities. Yes, if I flip three two times in a row, there is still an even chance that I flip heads and tails on my fourth flip. But if you have a coin that has flipped to the same side 15 times in a row-where, with a 95% confidence interval, I'll start getting suspicious after 6-I'm going to reasonably assume it's a trick coin or some other ruse. The randomness doesn't matter for the trick coin, because it's probability of landing on heads is 100%. It's "random" every time... But it will always be heads, because it's rolling a 100-sided die for it's outcome and every side has the same result. Random variable ≠ random chance; just because some things (like regular coins) are 50/50 doesn't mean everything is. But about the lecture question. The question says the prof has given a great many lectures, and they've all been interesting. "Great many" isn't a very specific term-it's a very large number, but large is relative. To be conservative, and for consistency's sake, let's say it's 15. Now, as you clarified, we have no knowledge on future events and cannot guarantee this Prof is always interesting. But if he's 15/15, we can reasonably assume there's some factor at play - maybe his charisma, his clear interest in the subject, the positive class environment - that strays this situation from a perfect 50/50. We can't say it's 100/0, but we can reasonably say it's something like 80/20 (5% boundary is at ~82/18; 1% boundary is ~74/26). If it were perfectly even, there is a 99% chance he has at least 3 dull lectures-there's less than a 0.005% chance of getting 15/15 by random chance. And of course, 15 was a very conservative estimate for the number of lectures. These probabilities would be even more insignificant if we increase to say, 50 lectures, which feels more befitting of the term great many. But we don't need to-past six (in either direction, 5 in one direction), we can reasonably assume some level of correlation. If you find something wrong with my reasoning plz lmk, but as of now I think the video answer is the most mathematically sound.

[@ambasing_omaygot]

9:39 It's either the primes (79, 47, 53) Or the multiples of 7 (35, 42, 63)

[@CertifiedGenius007]

I always overthink question like 4:28 At the end of 47 weeks, you have saved $282 At the start of the 48th week, you already reach $302 assuming your salary of $20 is credited at the start of the week. So should the answer be 48.xx weeks? (xx - when the salary is credited) Of course if the salary is credited at the end of the week, then it will take 50 weeks. So the question should mention that the salary is at the end of each week.

[@verkuilb]

In the 1920s, I’m pretty sure almost all salaries were paid AFTER the work was done-at the end of the week.

[@castleanthrax1833]

Yes, but it's not talking about when his salary is credited to him. He "earns $20 per week."

[@verkuilb]

@@castleanthrax1833 but he hasn’t SAVED it until he has RECEIVED it, and PAID his other expenses.

[@fron3107]

When he was paid at the end of the first week, then he could't have spend anything that week.

[@castleanthrax1833]

@@fron3107 Obvious they mean "he spends X amount of the salary from that week."

[@acaryadasa]

Another way of thinking about the sequence of 25,36,49,64,81 is that the difference between numbers 1 and 2 is 11. The difference between 2 and 3 is 13. The difference between 3 and 4 is 15, and so on. This will give you the same correct answer but without knowing that they are square numbers.

[@acaryadasa]

And here is why. If we want the difference between consecutive square numbers we can construct the formula (x+1)^2 - x^2 Expand this to x^2 + 2x + 1 - x^2. Simplify this and the difference between consecutive square numbers equals 2x+1. That means double the square root of the smaller square number and add 1. This will give a consecutive string of increasing odd numbers as the difference between consecutive squares. For example, between 25 and 36. 2x+1 in this case will equal 2 time 5 plus one, which is 11 which is the difference between 25 and 36.

[@ltdrak]

Del Monte is a food company. Maybe the other 5 were also companies in the time that test was taken?

[@GalaxyHomeA9]

9:35 i choose 35 53 and 63 because they 3 in common

@10:26 Gossard, Djer Kiss and Jonteel - each contain a double character

[@jeepien]

The more obvious choice is the three items that comprise two words each. Bon Ton, Djer Kiss, and Del Monte

@@jeepien From this perspective, someone else could choose the 3 names that contain only one word...

[@MrNostril]

I think brand names / countries question that you couldn't answer expose the problem with many qustions of the sat over time in that it's often not really testing your knowledge of language, but your knowledge of culture and therefore makes the kind of references that the types of people who make tests would be familiar with. I believe that probably the brand names you're supposed to pick out the brands associated with cosmetics and for the countries you're supposed to pick the 3 countries allied with the US in world war 1 (but it might also be balkans) and both of these associations are very eosteric 99 years later because culture has changed. But people with ample scholastic aptitude who existed outside of the kind of culture the test makers were familiar with would do worse because of these questions. Although in 1926 ensuring that peolle from the correct culture received educational opportunity may have been the point.

[@mrxmry3264]

10:46 i'd say bulgaria, greece and romania, because they're all in southeastern europe. BTW, you have a couple of typos in there.

[@patel_pankaj_69]

"4:38" i think ans. could be 48 weeks. 47 weeks * 6 per week = 282 Rs. Now, Add 1 week rs. 20 282+20 = 302 Rs. ≈ 300 Rs. Therefore, 47+1=48 weeks (Approx) Perfect ans. is 47weeks 6days 8 hours. [ 47.6.3 weeks ≈ 48 weeks ] I think so...🤔⚠️⁉️ @MindYourDecisions

[@aribellman1950]

How come the answer to the clock question is not 1836 seconds? 1800 seconds from the regular half an hour + the 36 seconds of the added time.

[@verkuilb]

@8:54, I’d say orange, pear, and chocolate. I like oranges, pears, and chocolate. The other three are disgusting. 😂

It would be interesting to see a statistic on how many students managed to solve this test. I would assume these questions were not that hard to those students.

[@jimhopkins9675]

The three most closely related terms are Djer Kiss, Mavis, and Jonteel, as they were all vintage brands associated with cosmetics, perfumes, and personal care products, often marketed for their luxury and elegance.

[@ollllj]

ANY numner always fits, if no "number of roots constrain" is given, which usually is not, becausae the function that firs ANY number sequence just needs as many roots as there are numbers in the sequence.

[@Amipotsophspond]

I have been playing around with the new deepseek local, I got it to spin out past it's context window. I was only using the smallest 1.5b so not that impressive. Anyway I think you and your viewers might enjoy how a human goes threw the question. basically it's just moving and rotating any quadrilateral so that it snaps to any point but the exact prompt is below. Please code a python function that takes in Snap point S, Quadrilateral Q, and Quadrilateral Rotation point QR. The quadrilateral is defined by quadrilateral corner point QA, quadrilateral corner Point QB, quadrilateral corner point QC, and quadrilateral corner point QD. each point has both a x and y coordinate. The function will return how much to move the Quadrilateral together with it’s rotation point QR and in degrees how much to rotate quadrilateral along the rotation point after moving, so that one of quadrilateral corner point QA,QB,QC, or QD is exactly the same as the Snap point S, without changing the quadrilateral shape. The function should start like this “def QuadrilateralRotationFunction(S,QA,QB,QC,QD,QR):” Then end return part of the function should look like this “return (QuadrilateralXMoveAmount,QuadrilateralYMoveAmount,DegreeQuadrilateralRotation)” if you prompt something shorter like, please code in python how to move and rotate a quadrilateral so that it snaps to SnapPoint different then it's AxisPoint. it miss understands the question and tries to rotate the quadrilateral using the snap point as the rotation point. so don't be fooled, by ai intentionally misunderstanding when it does not want to admit it does not know how to do it. On a unrelated note it's not that I don't know how to do the math of the problem I just don't know how to articulated the solution in a "elegant" way, lol. ok I don't know it, it seems so easy it has something to do with picking a corner point to snap, getting the angel and the distance to the corner point then getting the angel and distance to the snap point, then if the distance is greater then moving quadrilateral by the difference distance to the snap point but I am missing some trig steps and I am not sure what ones.

[@cameronwebb7964]

At 10:46, Roumania is spelt wrong, there is no u in Romania and also Norwary only has one r not two, the r appears before the w and not before the y, so someone failed with checking for spelling mistakes. Norway, Denmark, Japan because of only 2 colour with one being Red. Whoever was in charge of spelling mistakes, I hope has been fired for not doing their job properly.

[@yurenchu]

The flag of Norway has _three_ colours. However, the flags of Norway, Denmark and Japan each contain both of the colours red and white (but so does the flag of Bulgaria, although its red is a more brownish/orangish type of red). The flags of Denmark, Greece and Japan each contain only two colours, while the the flags of Norway, Bulgaria and Romania each contain three colours. The flags of Norway, Denmark and Greece each contain a cross.

[@yurenchu]

9:37 "79 , 35 , 47 , 53 , 42 , 63" -- Could also be the other three, {35, 42, 63}, because they are all divisible by 7 . In contrast, {79 , 47 , 53} aren't congruent to the same remainder class for any integer modulo > 2 . 10:35 "Bon Ton, Gossard, Djer Kiss, Del Monte, Mavis, Jonteel" -- Aren't {Bon Ton, Gossard, Jonteel} _French_ names? Del Monte is Spanish/Italian, Mavis is English, Djer Kiss sounds Arabic/North African. 10:46 "Norwary, Bulgaria, Denmark, Japan, Greece, Roumania" -- Norway and Romania are spelt incorrectly. That being said, Norway, Denmark and Romania use the Western/Latin script, while Bulgaria, Japan and Greece use a different script. 13:12 _Celestial_ doesn't refer to the stars, it refers to "heaven" (and _infernal_ refers to "hell"). 13:34 "obsequious, impudent, quiescent, fallacious" -- Could maybe be {impudent, quiescent} ? 22:10 "Conclusion: The next person who comes in will not like the picture." -- Seems to me the truth-value of this conclusion is _Undetermined_ : "admired" does not necessarily mean "liked".

[@kurayami4759]

10:48 i believe that the related ones are Djer Kiss, Jonteel and Mavis. The first 2 are cosmetics/makeup companies, and from what i was abke to figure out, so was Mavis. I couldnt find out if Mavis was a company/brand in the 1920s but the other 2 i know were

[@s.j.r7656]

Please solve this question for me. If the distance between the Moon and the Earth is halved, how many times larger will it appear?

[@yurenchu]

About 3 times larger (or 4 times as large). The diameter will appear approximately 100% larger (i.e. about twice as large).

[@StevenDietrich-k2w]

At 9:30 my answer was 35, 63, and 42 as they are all multiples of 7, while none of the others are. On the ones that puzzled you, I thought the Bon Ton one was that 3 or the choices were multi-word choices and the other 3 were single word choices. The Rumania-Greece-Bulgaria question I answered as those three are all on the Balkan Peninsula.

@9:35 I would go with 35, 53 and 63 as long as they are the only ones containing the digit 3.

[@steled03]

Arent Bulgaria, Greece and Roumenia sharing borders with each other ?

[@stefanosantoniades6344]

Bulgaria, Greece and Romania are all countries in the Balkans

[@psychette8846]

I am glad I live in Canada where education is pretty much the same where ever you live and therefore we don't need an SAT to evaluate the quality of people going to university.

[@donjoe7529]

shame that the questions were lost for the artificial language section; it looks like it could have been fun to try to reason our way through (minus the stress of an actual test situation, of course)

[@marthin-mainovinter5850]

I haven't watched the video, but the one on the thumbnail was pretty easy

[@Pawn-Sac]

6:45 is there an easy way to do this? Going from 36 minutes to 36 seconds seems too much a coincidence.

[@Pawn-Sac]

Oh! The denominator goes from 30 hours to 30 minutes (.5 hour) so 36 minutes will go to 36 seconds.

[@jeremiahlyleseditor437]

Accusative was right. The other three numbers all contained the digit 3 as well.

[@ЭмирБутимбаев-ц3ш]

While I was solving the puzzle from the thumbnail I found out that 3rd number will be equal to first number/3+ second number/3*2

[@Angi_Mathochist]

I think you are wrong on your last question in section 9. You can ignore (disregard) data that is unusual (outliers). I think the word that has been changed is "problem". I think the correct word there is "pattern". There are always outliers for any rule, and we can ignore them -- they do not disprove the general pattern. Your earlier word list: a bit of googling shows that those were all companies that make different things. I recognized Del Monte as a food company still in operation today. They may all have been current and well known at the time the test was made. Some of the names are of French decent or designed to sound French. That may be the key to grouping them. Or not. One made perfume and another makeup. It's possible that there were three that fell under the general heading of beauty or health products.

[@williamstier6445]

For the question of words in the mirror, it does seem worth noting that OHIO could be flipped upside down in the forward direction and still be the same (if it wasn't fixed to a wall that is).

[@acaryadasa]

Haha. Good point, if it were written like this: O H I O

[@yurenchu]

@@acaryadasa I think he means when the word is mirrored with respect to its horizontal symmetry axis: -O H I O- . This would have the same effect as when the sign with the word is rotated over 90 degrees: O ⌶ − O and you look in the mirror on the opposite wall: it looks the same as when you look directly at it.

[@jasiumater]

If f(x)=72x^4-936x^3+4302x^2-8163x+5475 then f(1)=750, f(2)=21, f(3)=264, f(4)=183, f(5)=210, so we can use this to predict what the next 2 numbers will be. They are: 2505 and 10956

[@howareyou4400]

For the question of the thumbnail, there is a very easy solution: *every number is the weighted average of the previous two numbers, with the immediate previous number taking a weight of 2* (750 + 2 * 21) / 3 = 264 (21 + 2 * 264) / 3 = 183 (264 + 2 * 183) / 3 = 210 ...