Math word problem from Who Wants to Be a Millionaire
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- Опубликовано: 4 окт 2024
- This is a math question from the TV show "Who Wants To Be A Millionaire?"
Which of these square numbers also happens to be the sum of two smaller square numbers?
(A) 16 (B) 25 (C) 36 (D) 49
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I can predict your mind 1:24
Not mine I didn’t think of that.
@@Gooooooomba you're an idiot.
(i didn't think of it either)
totally got me! ahahaha
Alternate meaning
Which of these is a pythagorean triple
I was just about to ask, isn’t this just a^2+b^2=c^2. As a land surveyor I better know this lol
@@TailicaiCorporation yes
That phrasing still wouldnt be entirely accurate because pythagorean triple refers to the set of all 3 numbers while here we are only looking for this biggest number in the triple.
@@Ninja20704 Exactly! And furthermore, in the Pythagorean triple, the numbers themselves aren't (necessarily) squares; while in this video, the question is asking which number is _the square of_ the biggest number in a Pythagorean triple.
By the way, a case could be made that (0, 1, 1) is also a Pythagorean triple, and furthermore that Pythagorean triples aren't necessarily a _co-prime_ triple; so (0, 4, 4) is, arguably, also a Pythagorean triple (albeit a trivial one).
@@yurenchu from what i know pythagorean triples require positive integers by definition so 0 isn't allowed.
You can feel the disappointment that BPRP is feeling during those few seconds of silence every once in a while 😂
my pfp is superior
I think the audience thought
2*2=4
4*4=16
And forgot how sum works
Or they wanted the player to get the it wrong
Yeah and bc 16 feels most correct from all of them at the first glace
Or maybe they were just being malicious because the question is damningly easy.
@@AverageCommentor Calm down Einstein
@@UndercoverDog
Not for me, I immediately ruled that option out
Remember, you have to study math because you might end up on a 90's game show where one of the questions might require basic arithmetic learned in elementary school.
Carpenters use Pythagorean triples to square up building foundations and stuff. A friend of mine called it "getting a hypotenuse."
Millionaire is always one of the best game shows in game show history.
Agree! And there have been so many dramas and stories from the show, too!
I understand that the answer the quiz master had in mind, was B: "25".
But, considering the wording of the question, all others (4²+0², 6²+0², 7²+0²) also fulfill all requested conditions, don't they? Just saying instead '... two smaller _positive_ square numbers' would have been an easy fit, wouldn't it? 🤔
In case I'm wrong, pls tell me why. Thanx 🙂👻
The term “square number” is refering to the resulting number after squaring, not the integer that you squared to get the result.
So 16 = 4^2 + 0^2 or 16 = (-4)^2 + 0^2 does not satisfy the criteria because the 4^2=(-4)^2=16, and 16 is not a square number smaller than 16.
@@Ninja20704got it, you are right 👍.
Thx for helping me out!
🙂👻
@@Ninja20704 the question omitted integers completely.
as we are in pythagorean territory a lot of solutions for _any_ of those 4 options appear and zero is not even part of the equation :)
for example
16=4²
9=3²
and the missing side for your rectangular figure would be square root of 5 (~2,236)
same shenanigans for a triangle made out of 4, 2 and square root of 12 (~3,464)
the question was worded poorly, but to mention "pythagorean tripels" would perhaps confuse the candidate AND audience
@@rivenoak the term “square number”, by definition, is a number that can be written as the square of an integer. So there is no need to mention integers because saying square numbers already means that we are restricted to integers only.
And honestly, people are even less likely to understand the question if it used “pythagorean triple” because a lot of math students have not even heard that term, let alone general public/audience
The 3-4-5 triangle wore off mr. ‘merican bro’s body
I remember this. Yeah B is made of 16 and 9.
Adding every odd number is basically each squared number.
Example: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64.
Damn this was something I didn't know even though I am a highschool maths student
@@prakharbharti3102
If you imagine starting with a 1x1 square, you see you can turn it into a 2x2 square by adding 3 squares around the outside. Similarly turning a 2x2 square into a 3x3, you would add another layer along the outside in an L shape. That L shape would add 2 on top, 2 on the side and 1 on the corner. Every time you want to go up to the next square, you have to use 1 more block to the top of the L shape and 1 more block to the side of the L shape. So the L shape increases by 2 each time, giving you every odd number.
And in general the difference of two consecutive squares is written n² - (n -1)² which we can do some algebra on:
n² - (n - 1)² =
n² - n² +2n - 1=
2n - 1
which is a formula that returns odd numbers when n is an whole number.
🤯
@@prakharbharti3102 It makes sense if you visualize it - if you imagine you have a square, and you're adding 1 to both the length and the width of the square, you can see that the area of the square increases by 2*the current width + 1 (the vertical rectangle and the horizontal rectangle being added both have an area of the (current width + 1) *1, and then you subtract 1 from that because of the 1x1 square where the horizontal and vertical rectangles intersect to avoid double counting that section)
That pattern is basically just repeating that step over and over again - you start with a 1x1 square, and each time you add the next number in that sequence you're adding 2*the current width +1, which as shown above is the difference in areas between a square and a square with that width +1, which naturally when summed with the area of something that's already that square will give you the area of a square with 1 greater width.
So the next one that's the sum of two square numbers is... 12²+5²=13²
Always going to be the square of an odd number to increase the root of the the other square number by 1.
And _which_ square number does it increase? Well, it increases (((odd number)²-1)/2)² to (((odd number)²+1)/2)².
1²+0²=1²
3²+4²=5²
5²+12²=13²
7²+24²=25²
9²+40²=41²
11²+60²=61²
13²+84²=85²
15²+112²=113²
+2 +32(+4) +32(+4)
...and there's the full pattern. Not _every_ Pythagorean triple, but all the ones where the length of the hypotenuse is 1 more than the length of the longer side.
A is the result of squaring a (natural) number twice ( 2² = 4 , 4² = 16),
B is the sum of two smaller square numbers ( 3² + 4² = 25 ),
C is the product of two smaller square numbers ( 2² times 3² = 4 times 9 = 36),
D can be summed with a smaller square number to result in twice another smaller square number (49 + 1² = 50 = twice 5² ).
A is 4^2, B is 5^2, C is 6^2 and D is 7^2. So, them being consecutive could've been another reason they were chosen.
@@Quadratic4mula I wasn't trying to provide a reason why those numbers were chosen by the question maker; I was listing possible ways in which the contestant could (mis)interpret the question and choose either number as his answer.
Note that in each line, the answer option is construed as the "end result" (or "product" or "sum" in their non-mathematical sense) of an operation that involves (at least): two smaller numbers, and performing the square operator twice; which are the key ingredients that are present in the wording of the question.
@@yurenchu Your expansion on D does not fit in line with your thing about two smaller numbers and performing the Square operator twice. 49 is not smaller than 49.
@@Quadratic4mula 1 and 5 are smaller than 49.
In fact, 1² and 5² are squares smaller than 49.
It is _literally_ present in the line written for D:
"D can be summed with a *smaller square number* to result in twice *another smaller square number* "
@@yurenchu You said the result (sum or product). 1 and 5 don't sum or multiply to get to 49 whether you square, sum, or multiply them in the way that you did.
At first i was confused then i saw the word sum. Most people will probably unconsciously ignore that word hence the misunderstanding of the question
Yeah it’s real easy to jump to the wrong conclusion here.
Standard lesson to learn here - Read the question carefully!
Pythagoras: what is this guy’s problem??
idk why I assumed the two smaller numbers had to be the same numbers
That was my mistake!
Nah fr, my dumb ass was like,"Shit, we gotta go to decimals now??" 🤦🤦
@@commanderwaddles3483 😂
ok, it works for any square figure, where hypotenuse is the diagonal line and thus a valid solution of pythagoras by default.
unfortunately such diagonal is a multiple of "root of 2" and thus irrational OR the sides are of very odd numbers so their combined square results add up to a smooth number.
That's what I assumed at first, then I realized nothing says that and a few seconds later I got the right answer.
This shows that people with photographic memory aren't always great at logic
Absolutely NAILED the "disappointed Asian dad" look, made me feel bad even though I got the question right
If he was Singaporean, he would have lost his passport on the spot!
The question reminded me of 3 4 5 triangle
Well technically all of them are the sum of smaller square numbers (infinite amount). Now if it said two smaller square integers, all are still answers, as for like the first -4 and 0 or 4 and 0. Only when you restrict it to positive integers (natural numbers) then B is the only answer.
-4 squared is 16, which is not a smaller square number than 16, and so does not satisfactorily answer the question.
@@michaelfaccone5811 I was thinking smaller number, not smaller squares. Yep your right. so restrict to integers is enough
@@ingiford175.
Any square number would have to have integer roots - 8 (random example) is not a square number as it doesn't have an integer root, so restricting to integers is implied in the question.
a square number is an integer that is the square of an integer. So by definition its always going to be an integer.
this fuels my toxic trait thinking i would cheese this show
Great short video!
It’s funny how there are always comments like “Everyone knows this” nope. That’s is perfect example of how most people just don’t know these little things lol.
This took me way longer than it should have but maybe it's because i'm tired
n^2=(n^2)+(0^2), but (n^2) is not smaller, than (n^2)
First thing I thought of when I saw the thumbnail was the 3,4,5 right triangle
0:00 I looked at this for one second and instantly recalled the smallest Pythagorean triple
No ammount of TV stress can justify a mistake this horrible
Yes, it can, if you understand, how stress works: it blocks conscious thinking, because it is slow anyway. When it is time for action, fast thinking is needed and that it will have fast access to your senses, which is not the conscious part of your brain.
And it also blocks all the feelings, which may distract you, like eg. pain.
So in such a situation it depends a lot upon how stressed you will become. This can vary a lot between people.
The interesting part is more, why we do react with stress in such situations as if we would be attacked by an animal.
Nice one, I thought the two smaller squares should be equal to each other, so I couldn't answer it
Math is always useful in life.
I've seen this video on your Instagram. This is what I think: since a number can be expressed as a sum in an infinite number of ways, isn't it possible that all four of those numbers can expressed as a sum of two smaller square numbers? Now if we actually mean perfect squares, that's a different thing.
Square numbers, by definition, are squares of integers.
That's a tricky problem for on the spot.
16,9,25 standard right angle triangle of 3,4,5 which I see daily so answer is 25 , and also angle is 54,36,90 if I remember
53,37,90 i think 😅
@@اشکانمحمدی-ز1ث oh yea thanks you are correct
36.86989 ... = arctan(3/4)
and the other angle is 90 minus that one.
Theoretically all of them could be correct (refering to the cuestion that appears on the thumbnail of the video), because it doesn't mention that the numbers must be whole numbers, but the question is understood.
“Square number” means the square of an integer by definition. So only 25 can be correct
Being a mathematics person and watching old game shows on the yt, I especially _cringe_ (likened to bprp’s moments of silence) at incorrect mathematical answers. Especially on quiz show ones like Millionaire. 😬😬😬
You are my math class
2 tesseracted=2⁴=16
What'swrongwith 16=0²+4²
Correct me if i am wrong
3^2+4^2=25 B) final answer
Me 25 = 5^2 so the smallest pythagorean triplets are 3,4,5 so 3, 4 => 3^2 + 4^2 => 5^2 :)
I have to admit, it took me way too long to even understand the question correctly.
I just had to think about square numbers and if they do have to be an integer... But I think they do, right? Otherwise there would have been countless solutions.
Anyways he is just one away from a right answer
I'm not aware of anyone who teaches "square numbers" meaning anything other than perfect squares. IOW, I don't think anyone would call 8 a square number, even though it is the square of sqrt(8).
Square numbers, by definition, are the square of an integer.
So yes, you must use integers only.
If you are allowed to use all real numbers, then every number is a square number because sqrt is an operator on the reals.
The people who chose A probably thought that 0⁰ = 0. When in reality, it's often considered as "Undefined" or even 1 in some cases.
As if simply "paying attention" were already enough to "know maths"...
quick question: when i saw this video, I was like "hell no, there are infinite answers. how are we supposed to find the correct answer?". But the question had an answer which baffled me. you could get 25 as the sum of squares of square root of 24 and 1 which are smaller than 25. so you could take sum of squares of any two real numbers to get the sum 25. so basically aren't there multiple options for it??
The question also doesn't specify the numbers as perfect numbers.
so technically I am right, right? I find this disturbing the sanity of my mind. Pls do correct if I am wrong.
Square numbers are defined by being the square of integers. 24 is not a square of an integer and so is not a square number, even if it does have a root. 16 and 9 are the only square numbers that sum to another square number, 25, in those 4 listed options.
“Square numbers” by definition are the square of an integer.
Because if not, we can say any number is a square number which would make it completely meaningless
Idk how ppl dont know basic maths, like they take education for granted perhaps
4× 4+ 3× 3= 25
Remember pytha numbers to get it done instantly
the question omitted the requisite of integers, so all 4 options are true by default.
what the show really wanted was a pythagorean tripel, but did not say so :(
“Square numbers”, by definition, are the numbers that can be written as the square of an integer. So saying square numbers automatically restricts to only integers.
What surprises me most is that 70% of the audience don't know this.
16 can also be correct. 4 squared plus 0 squared. 0 is a square number. It should have had the word "positive" at the end of the question. Then, 25 would be the only correct solution, since 0 is not a positive number.
At last. 🎉🎉
1:24
16 is not a smaller square number than 16.
The question said two SMALLER square numbers. 16 is not smaller than 16 so 16 = 16+0 does not satisfy the criteria in the question.
I got an A in math in high school its been 4 years I dont remember any of this😅
Remind me of pythagoras class
Phone a friend! (If your friend's name is Pythagoras)
Just looking at it, it's
B, 25. 16 + 9 is 25.
Smart
I misread the question damnit lol
Never mind
Me being a smart ass on TV: "I assume by two smaller square numbers, you actually mean two non-zero square numbers otherwise the question doesn't make sense"
Actually works fine either way. In "16=16+0", one of the two numbers after the = sign isn't smaller than 16, and the other one is 0.
He could find the answer if he subtracted one of the choices from the others. 25-16=9.
Assuming he knows what square numbers are, and that he would have recognized 9 as being a square number.
0.10. To get another 15 000 dollars? The number in right corner says 16 000... Now I'll watch the video.
Because he still walked away with $1,000 😃
Some people mistook sum with multiplication 💀
3squared+4squared=5squared 🤯
i’m actually shocked, how can people not know this. Even a fifth grader can answer this question 😭
The contestant knew that he didn't know the answer; he should have decided to walk away with $16,000 instead of taking a risk. (Unless he already has a fat bank account and $16,000 is nothing to him.)
3-4-5 tripple, obv 🙄
What also could have happened is that the viewers have misunderstood the question since some may have interpreted it as "Which of these numbers is a square of a square". Incidentally, that's what I was immediately thinking before I realised the question actually meant "Which of these numbers is a Pythagorean triple" and in turn made me immediately realise the correct answer.
Homie lost money due to basic math
Its not so much of a math problem. Most people that know the right answer just know it because they have seen it before so many times. They dont have to actually do any math to get it.
25, 16+9=25 (i answered before I watched)
The question is technically wrong as all of them can be sum of two smaller integer numbers as in (16 = 4²+0²) , they should mention natural numbers 😂 lol
Edit: definition of square number by wikipedia: In mathematics, a square number or perfect square is an integer that is the square of an integer;[1] in other words, it is the product of some integer with itself.
And 0 is an integer.
The question as written required both of the square numbers being summed to the answer choice be smaller than the answer choice. 4 squared is not smaller than 16.
The question asked for two SMALLER square numbers. So 16 = 4^2 + 0^2 does not satisfy that crietria because 16 is not smaller than 16.
1:24
Dude committed two errors:
1. Didn't pay attention in math class (and didn't watch bprp videos).
2. Consulted audience for a math question. Many people sadly suck at even the most basic math.
and _third_ error:
3. Decided to take a gamble on a math question, instead of walking away with the $16,000 he had.
(By the way, to all the math people and statisticians out there: Yes, I'm aware that the _expectation value_ of his return is arguably greater if he "plays" than if he "stays".)
@@yurenchu I see what you're saying but I wouldn't call it an error per se. Any gamble on Who Wants to Be a Millionaire is, well, a gamble.
You only know whether it was a mistake to make the gamble when the answer is revealed.
Colloquially speaking, it will have been a mistake if he loses, and a good decision if he wins.
The way the question is written does deliberate hide the fact that it's about geometry and pythagorean triples. Clearly it fooled a lot of people in the studio audience. It's like those "word problem" type of questions where the first thing you have to do is understand the question so that you can translate it into the right maths to solve it.
It doesn't necessarily have to be about geometry and Pythagorean triples. I didn't learn about right triangles and Pythagorean triples until high school, but I did learn at elementary school what sums and square numbers are.
my braining thinking 4+4 = 16
So i won $16,0000 right...?!!
Why DOESN'T zero count as a number? You're insisting the answer be solved with a *triangle*, but it doesn't have to be.
It does, but it doesn't work as 0^2 is 0 so the other number has to be equal to the answer, and therefore cannot be a smaller square number.
1:24
The question asked for two smaller square numbers. So if you let one of them be 0, the other number would have to be equal to the original, violating that condition.
Being old school, I knew this off the top of my head. Enough about me; let's slam the American adults.
Only 30% of the audience got it right. So 70% were incompetent. However, it's probably worse than that. 25% would get it right if answers were chosen randomly. So that's 5% better than complete ignorance.
all answers are correct unless the answer has to be the sums of positive, different integers
No. "Square numbers" are the squares of integers, otherwise the word "square number" would have no meaning at all.
@@ThomasVWorm nuh uh
@@BTRequiemOfficial “square numbers” are by definition the square of an integer.
You cannot say 5 is a square number because it is [sqrt(5)]^2 because sqrt(5) is not an integer. Not even 4/9 even tho it is (2/3)^2
Without this restriction, having the term square number would be completely meaningless and pointless because every number would be a square number.
While we usually only call the numbers with whole number roots square numbers, technically all numbers are a square of something, so one could argue that all answers are correct :D
(2 is a square of the square root of 2, meaning that 2 is a number, which is a square of another number)
The term square number is by definition the square of an integer, not just “usually”. Nobody ever says 2 is a square number for example.
Otherwise every number is a square number, making it completely pointless term.
@@Ninja20704 Of course you're right, I just wanted to stretch it for fun
Good job ignoring 👍🏼👍🏼
I remember that episode. It was so crinchy! He took forever and then still chose wrong on a question any 10yo can answer.
ah yes my favorite word, crinchy
@@devookoC R I N C H Why
You’re a mean one Mr. Crinch. 😂
I swear man every asian kid can solve this piece of cake within 5 sec . Can't believe the majority of grown ups couldn't solve a 8 grade question.
It wasn't stated if zero could be taken 4² + 0² is 16
@@PranitSuman no need to state. Zero _is_ a square number? c'mon mate.
@@VectoRaith No I mean it wasn't stated if we had to take natural numbers or integers
@@PranitSuman Oh, I see your point now...
@@PranitSuman It doesn't matter. 4^2 is a square number but isn't _smaller_ than 16 .
who said the square root of 8 isnt a number
Who even said it wasn’t
ruclips.net/video/i7qoq3KQiaw/видео.htmlsi=RSz4GLMNiDpKScra
A more meaningful answer for your math students who ask when they'll ever use calculus in real life.
A 12 year old can easily solve that question ☠☠
... But it takes someone with more maturity to have compassion for a person who cracked under stress.
His remark is probably directed at the audience of whom a large majority did not vote for B @lornacy
@@liamschreibman8268 Yeah, I can accept that😁
@@lornacy It was 50%, so it was not what would be called a _large_ majority (or even a majority at all).
I get (and agree with) your point, though.
EDIT: My bad, you said "a large majority did not vote for B", and not "a large majority voted for A, the answer that the contestant gave". 70% is indeed a large majority. I misread your post. My apologies.
EDIT 2: I've now noticed that I have replied to the wrong person: my reply was meant for @liamschreibman8268 , instead of @lornacy . So it appears that I've been making quite a mess of my post! Again, my apologies.
What'swrongwith 16=0²+4²
Correct me if i am wrong
What'swrongwith 16=0²+4²
Correct me if i am wrong
What'swrongwith 16=0²+4²
Correct me if i am wrong
The Question demands that the number is the sum of two smaler square numbers and 4² is not smaler then 4². And if that solution would be possible every answer would be correct.