I got it in 30 seconds, that is a question that shouldn't be in a 4th grade classroom lol

3=0.8, 4=10, 5=5, 6=6, 7=7.333r

80% 0.8^3 = 51% or 0.5^(1/3) = 0.79 square cube rule to go from height to volume

4 right angle triangles, all having the unshaded side in the center

Solved it in 10-15 mins

My question is where does she buy her “dr” title or “phd”

The proper answer to the question is first to define what a corner is and then give your answer. You missed the obvious answer of 4.

I made a circle understanding that sin(45) and cos(45) is √2/2 using this to get the corners of the inner cube then shading the outer one. Works but more complicated then the simple answer

Curse you math and physics!

If you see this question, just remember puzzle box & pinhead or Baseball Diamond

I got curious and simulated this in python. My game dealt both players a card between 1 and 100 (because I wanted more scope than just 6 cards) players independently choose to swap or keep their card based solely off of it's number, if both choose to swap then they do so. I set up a competition with 10 players: Player 1 - would swap any card below 90 Player 2 - would swap any card below 80 (continue in the same way...) Player 9 - would swap any card below 10 Player 10 only swaps on a 1 - as suggested by game theory. After 1,000,000 random games against each other, the player with the highest total win percentage was Player 7 (swaps any card below 30), with 55.8%. However, the only player with a positive win % (albeit very small) against all other players was Player 10. So this is the strategy that will beat any other strategy on average. I found it quite an interesting exercise - it helped me make better sense of the video, two perfectly logical players should only ever swap a 1 (which means they never swap) but it goes to show that the 'best' strategy depends on the other players. For example, I re-ran the test with only the players who would swap below 50 and Player 9 - who would swap 10 or below came out best.

Did I miss something? How did he get 32 for h squared? I don't see it...

But what if you asked a student to prove that one of the non-standard solutions are, in fact, a valid solution?

💀

Goofy ah 1980s song moment 💀

to me the 3 corners were the 2nd most natural answer (after 2) due to this: a semi-circle is basically a 180deg pizza slize and pizza slices of angles >180 and <180 both have 3 corners, so a 180 pizza slice does have 3, it's just that one of them is 180 degrees

This only works if the bottle is completely full (this is not stated, so may be not the case) You have two separate heights .... add together and minus the height of the bottle. This gives a true cylinder of 5 Cm so Pi r squared gives the volume of excess and take that off the full volume and you get your actual volume. Alternatively you can find the 5 cm figure .... half it and that is your 50% of the full bottle .... then add the additional 2.5cm x Pi R squared to get your actual volume.

I got 27. Because 2+7 is 9. Lila is 9. After 5 years, she will be 14. 2×7 is 14. It says "her math teachers age at that time," but it doesn't specify what time is "that" time... So I think that is my error...

Me : “ hehehe… I KNEW IT !!!!!!! IKNEW ITTTTTTTRT”

Before watching the video-assuming the length of one of the smaller squares is 1 unit, the only solution I can think of is to shade it so that the unshaded square has an area of two square units, meaning each side would need to be the square root of 2 units long (about 1.4u). This would mean that the amount of area shaded would be 2 square units as well. However, I DEFINITELY didn't know what a square root was when I was in 4th grade lol Edit: I got it right! Woohoo!

For me: 11.56 = 1156/100 Then, I'd use prime factorization: 1156 = 2 x 2 x 17 x 17 = 2^2 x 17^2 = (2 x 17)^2 = 34^2 100 = 2 x 2 x 5 x 5 = 2^2 x 5^2 = (2 x 5)^2 = 10^2 Therefore, the square root of 11.56 = 34/10 = 3.4

I got 27?.. 2+7 is 9 9+5 years is 14 2×7 is 14...

If he always lies then I assume he lied

Ye I noticed the blue part when I was highlighted

bro the infinite chocolate is fake

The problem with the solutions that aren't the first are that there's no good way of nailing the area for a 4th-grader other than eyeballing it. I just don't see them solving a quick square root of the side length. That being said, I first thought of the second solution but I wasn't sure how close to 1/2 the teachers were supposed to let slide.

Numberphile just did a video on this same topic (although asking a slightly different question about the volumes), including physical props to see the effects IRL: kzfaq.info/get/bejne/g9GeZrOrycemqY0.html

I don’t have a mathematics background so forgive my ignorance here, but couldn’t you show that the the hypotenuse^2 is equal to a^2 + b^2 by making b^2 infinitely small, which would make the triangle approach a flat line at which point the hypotenuse and the remaining side are equal. This seems too simple though, so maybe someone can’t point out why this wouldn’t work.

The mom: After one hour 1 hour I found no solution This guy: After a few seconds, I have 48 answers, which do you prefer?

Hrithik Roshan: Sorry Sir, it does not work for me! 😂

Honestly, once I actually understand the question it was really easy. However, I had no idea what the question even was. It was written extremely poorly for sure.

I like the 4 corners one better than what i came up with, my solution was shade half in the shape of a square in the middle.

Idk it seems easy just measure the diagonal of the smaller square and using some pythagoras stuff , u will get that it is equal to side of bigger square /√2 then use that to draw a square inside the square

Another reason to choose "egg" as the odd one out would be to note that it is the only word there beginning with a vowel.

lowk i’d just shade the edges until half of it is shaded and it has a square in the middle idk 😭

How is this even hard? Seriously, if you couldn't figure this out in the first 5 seconds, it's not the schools that failed.

Thank you for providing two more reasons to avoid Wolfram Alpha. Two incomplete, i.e., wrong, answers.

Interesting that both possible solutions are the golden ratio.

Remember, you can always take the whole chocolate and shove it down your mouth and say "It's just a prank bro."

This feels like one of those questions the book author thought was so clever but in reality it was just a terrible idea that probably confused all but the smartest kids in the room.

Bros teaching us math on summer break 😂😂

Just leave a square of root 2 by root 2 blocks unshaded

Yeah, took me about 2 minutes of real thinking

I was in the 4th Grade in 1960. I must have been in a Class for "Slow" Students. We didn't learn the basics of Plane Geometry or Squaring Numbers. We were just Learning Simple Fractions. It's Great to Hear that Schools are now Really Teaching Higher Education. I Guess Graduating High Schoolers are All Leaving with Degrees. Tax Dollars Well Spent😀

Not mentioned for kids at which levels. For really early young learners, D should be the intended answer. For more advanced learners, A should be the intended answer. But if D was the intended answer, then the question was asked wrongly. Should have been "What time is closest to midnight" or closest proximity to 12am on the clock. "What is the closest time to midnight" refers to the time needed getting to midnight and so B & D being just past midnight will take a longer time to get to midnight.

My friend had a silver toothbrush on his desk. Then egg should be out

Just shade the corners on the outside and create a diamond or I would say, rotated square. Seemed pretty straightforward. 😅

When you know the lenght of the chords as shown in method 3 then 4R²=30²+12²+16²+(45/2)².

The ratios of an area is a function of the square of the shape and for a volume is the cube of the shape, whatever the shape, so far as it is regular - simple. The maths proves it in a very convoluted way.

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