This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .

Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.

Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold

- bulleted - list

bulleted

list

1. numbered 2. list

numbered

list

Note: you must add a full line of space before and after lists for them to show up correctly

My country's national olympiads 1st round is to be conducted tomorrow. I will most likely post all of them here for our consumption! I expect them to be pretty easy.

@Ekene Franklin
–
No. At present I am not interested. The main goal of student student studying in class 11 and 12 in India is to get into IIT (Indian Institute Of Technology)

This is a marvelous secret and I benefited a lot from this. If you want to write any question for the problems of the week the better option is to write a physics problem rather than maths. Out of 5 problems 3 are allotted for maths and 2 for science. In the maths category there will be a much competition from many users. But in the science category there are only 4 competitors namely Rohit Gupta, Pranshu Gaba, and two staff members Blake Farrow, Danielle Scarano. So, I posted some good physics problems and 3 of them are featured now. But I won't force you to post only physics problems then there will be much competition for science. If you have good problems in maths you can post them (as 3 of my maths problems are also featured although I say that I am basically a physics man).

It will be in the main option bar. It is the place where you can find links like "profile", "stats", "search", etc. The "view" full site option will be present there.

@Mr. India
–
Ohh !! You are doing in the app. Sorry, I don't know whether this is possible in app or not. But can't you find any option like this. in the screenshot.

@Mr. India
–
In every set there will be a option at the bottom called "save". If you click that, that particular set will be saved into your sets. Some of my problems are original whereas some other are completely taken from books or the problems and the remaining are the problems which I have taken from books and modified them.

@Mr. India
–
The community members write problems and post them to community and the staff selects the best 15 questions among all the problems and they will feature them as problems of the week. There is no forum involved in this process.

Before brilliant used to have biology. But recently when the staff updated brilliant they removed biology topic due to lack of problems in that category.

Hello Everyone !!! As this note has got some immense response from young students I would like to continue this further. But the problem is that this note is getting more and more comments day by day due to which the process of loading and opening any notifications is taking more time. So, on the request of @EKENE FRANKLIN any further discussion can be continued in the new note Brilliant young students messageboard

If the mole fraction of a solute is changed from $\dfrac14$ to $\dfrac12$ by adding some solute in the $800~g$ of $H_2O$ solvent, then what will be the ratio of molarity of the two solutions ?

Simply balance the redox equation and substitute the stoichiometric coefficients of the balanced reaction into your expression.( I would have posted a solution if only my device could type LaTeX.)

I don't think uncertainty in position and momentum are relativistically equal. However, if a non-relativistic assumption is to be made, then from Heisenberg's, and taking p=mv, then uncertainty in velocity>=(h/2pi)X(1/(uncertainty in position X mass)). Sorry for the math ambiguity. My device doesn't type LaTeX.

I have an answer, but I am not totally sure it is correct. Coordination structure chemistry of silicates and silicones is my weakest point in chemistry. Perhaps I need to practise more!:)

@Ram Mohith
–
My goal in many interactions is to make them frictionless. Trivially speaking, I resist every enmity and conduct friendliness. I have even successfully transmuted people from an angry ground state, to a happy excited state!

Quantitatively speaking, momentum is the product of mass of a body and its velocity. It is denoted by $\overline{P}$.
$\large \overline{P} = m \overline{v}$
But the above definition is valid only when velocity of the body is constant. If the velocity of the body is variable we cannot use this formula and we should go by calculus. Physically speaking, momentum is the rate of change of kinetic energy with respect to its velocity. So, you ca say it as kinetic energy at that instance. Here is how we get $\overline{P} = m \overline{v}$ from kinetic energy.
$K.E = \dfrac12 m (\overline{v})^2$
Now, differentiate both side with respect to velocity. We get :
$\dfrac{d}{dx} K.E = \dfrac{d}{dx} \left ( \dfrac12 m (\overline{v})^2 \right )$
As, we know $\dfrac{d}{dx} K.E = \overline{P}$, we get :
$\overline{P} = \dfrac12 \cdot m \cdot 2 \overline{v}$
So, we get :
$\large \boxed{\color{#3D99F6} \overline{P} = m \overline{v}}$

I think you have posted many problems in brilliant. However, when you are writng a question there will be two options, either Number or Multiple choice. You can select whatever you wish.

Thanks. The results will be uploaded online in about 1.5 hours. Meanwhile I am posting them here for our consumption. Solve some, post solutions and invite others to do same!

Problem 1:
A password consists of $4$ distinct digits such that their sum is $19$ and exactly two of its digits are prime, e.g. $0397$. How many possible such passwords exist?

There is a trick. First, take the 20th triangular number. $\displaystyle\frac{20(20+1)}{2} = 210$
Add 1. $210+1=211$ These numbers are known as pizza numbers and are always one more than a triangular number.

@Ekene Franklin
–
Since the divisibility rule of 5 only concerns the last digit, we have to find the last digits of the values. $1^{124}$ is obviously 1. Since the repetition in the last digit is (for 2): 2, 4, 8, 6 then $241 \div 4 = k (\text{Remainder}1$) the first number is 2 (in this set). Apply this to the other powers. Summing the last digits, we get 10 and $10 \div 5 = k (\text{Remainder}0)$

@X X
–
Not exactly what I did, but something similar. Thanks a lot. If I may ask, have you ever participated in an olympiad before, or do you hope to participate in one?

@X X
–
Ok. Thanks. By the way, I really admire your problems. They are very cool. One of my major problems here is creating problems. My original problems are too easy(you can check them out). But solving others problems(of course not those extremely hard ones) is not a big problem for me.

@Ram Mohith
–
You're right! (Ha, ha! I'm a little jealous of you because your problems are often the first problem in the easy category, and in your contributions page, the number of people are banging up:p)

@X X
–
But I am not fully done. I expected that Number + Reciprocal will take me to 1 lakh (100 K) solvers. But it fell short of 7 K. But luckily this week too my question came in one of the problems of week (the first one) so it is confirmed that I will reach the milestone in one or two days.

@X X
–
Yes, Vamprie Fan Club. It is were I had my first individual century. After that, the next week I had got 150 upvotes for my question Rising Balloons and the next week is a memorable for me, as I had my first double century for the question Counting 0's.

I have made a hatrick in June 9 - June 29 (3 weeks) as 3 of my problem continuously came in easy part of the POTW. Now again the chance has come for me. Last week and this week too two of my problems are featured. So, if luck favors next week to I can have a problem in POTW. I am thinking very hard on which question should I post the next.

@Mohmmad Farhan
–
No. Still under construction. Before that one I have two more questions, Raising Balloons - 2 and Popping balloons which are yet to be released. After these two the sequel for My. Everest vs Mt K 2 will be released.

Thanks a lot. But no one apart from us is solving the problems. I want to check my solutions and my faulty areas. Please direct the problem solving masters of Brilliant here to help me out.

@Ekene Franklin
–
If you want to direct anyone to this place just keep the symbol @ and type the name of the person. Immediately a notification will be sent to that particular user.

I think you there is some error in spelling or you have kept a gap between the symbol and name. Once check again. If it is correct then you should get it in blue color link and not just normal text.

For example you should type it as @ _ Ekene Franklin ( _ symbol means no gap) then you will get it as @EKENE FRANKLIN

@Ekene Franklin
–
You should select from the list which will appear when you type the name. Also the name should be exactly matching with that particular user even capital letters should be taken into consideration.

My first trophy was in Grade 1(third)[english], Second in grade 2 (1st)[first scrabble competition] and third in grade 2(Best school player award)[first scrabble competiton]

I have a proof for the existence of infinite dimensions.

On a line (1 Dimension), a number can be represented by a point. On a grid (2 Dimensions), an intersection is represented for the data in a cell. In a cube (3 Dimensions), data can still be represented on a point (where straight lines intersect). Following this pattern, there are infinite dimensions (because there are $\aleph_0$ numbers).

Exactly. Just what I did during the exam, using the logic that if a prime satisfies those conditions, then the only even prime, 2 must be in the sum and difference.

@X X
–
I think you must minimum have 5K people reached. But the main parameter I think is that the contribution page is mostly obtained either by up votes or by solvers to the question (more than 1K). When I got my contribution page I have around 120 upvotes, around 300 solvers, around 30 views for my notes.

@X X
–
@X X, I want your help. I am trying to write a new problem but I got struck up at one point. Here is my doubt :

Suppose lets say a man jumps from a building with initial velocity $u$. After $x$ seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did :
$ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2$
where $t$ is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as $(t - x)$ or $(t + x)$.

@Ekene Franklin
–
And also due to the high specific heat capacity of water. This question is a slight modification of air currents (due to which it is cool during the day and warm during night near coastal areas) and I am going to post this very soon.

Hello to everyone! I have not been around for some time now on Brilliant. However, I met on my return a delightful change in the method of posting options for multiple choice questions on Brilliant. Kudos to Calvin Lin and the truly brilliant Brilliant team!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestMy country's national olympiads 1st round is to be conducted tomorrow. I will most likely post all of them here for our consumption! I expect them to be pretty easy.

Log in to reply

Ok. Thanks and also are you writing that exam.

Log in to reply

It is actually meant for students two years older than I am, but I will give it a shot.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

This is a marvelous secret and I benefited a lot from this. If you want to write any question for the problems of the week the better option is to write a physics problem rather than maths. Out of 5 problems 3 are allotted for maths and 2 for science. In the maths category there will be a much competition from many users. But in the science category there are only 4 competitors namely Rohit Gupta, Pranshu Gaba, and two staff members Blake Farrow, Danielle Scarano. So, I posted some good physics problems and 3 of them are featured now. But I won't force you to post only physics problems then there will be much competition for science. If you have good problems in maths you can post them (as 3 of my maths problems are also featured although I say that I am basically a physics man).Log in to reply

Where is the show full site option??(from ur mt. Everest Q discussion)

Log in to reply

It will be in the main option bar. It is the place where you can find links like "profile", "stats", "search", etc. The "view" full site option will be present there.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Here is the screenshot of where is it present. Can you find it now ?

Log in to reply

Log in to reply

Log in to reply

How do you send questions to them to select for weekly problem??Do they themselves select from your sets?

Log in to reply

No. Only staff will select the problems of the week. In general, the notification will be as if I have written the problem of the week.

Log in to reply

Log in to reply

Log in to reply

I personally think Brilliant should include a biology and biochemistry section. What do you think?

Log in to reply

Yes.

Log in to reply

Before brilliant used to have biology. But recently when the staff updated brilliant they removed biology topic due to lack of problems in that category.

Log in to reply

Actually I asked them to remove it, because the biology problems could not be seen in the community page. You can see Calvin Lin's messageboard.

Log in to reply

Log in to reply

link. It's still available.

Really? Here is theLog in to reply

Log in to reply

yes

Log in to reply

Here is a link of a biology problem.

Log in to reply

Yes, but they cannot be found in the community page.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Those are from a set biology is so easy-2, biology is so easy-3, biology is so easy-4, biology is so easy-5biology is so easy-6, biology is so easy-7, biology is so easy-8, biology is so easy-9, biology is so easy-10, biology is so easy-11, biology is so easy-12, biology is so easy-13, biology is so easy-14 by Mohammad Khaza.

Log in to reply

Hello Everyone !!! As this note has got some immense response from young students I would like to continue this further. But the problem is that this note is getting more and more comments day by day due to which the process of loading and opening any notifications is taking more time. So, on the request of @EKENE FRANKLIN any further discussion can be continued in the new note Brilliant young students messageboard

Log in to reply

$\text{Doubt : 1}$

If the mole fraction of a solute is changed from $\dfrac14$ to $\dfrac12$ by adding some solute in the $800~g$ of $H_2O$ solvent, then what will be the ratio of molarity of the two solutions ?

Log in to reply

$\text{Doubt : 2}$

In the following reaction : $\large aNO_3^- + bCl^- + cH^+ \rightarrow dNO + eCl_2 + fH_2O$ find the value of $\dfrac{a^2(b + c)}{d \times f}$

Log in to reply

Simply balance the redox equation and substitute the stoichiometric coefficients of the balanced reaction into your expression.( I would have posted a solution if only my device could type LaTeX.)

Log in to reply

Ok. Try now after keeping it in \ (....) without spaces which will give you $...$

Log in to reply

Did you tried it. What is the answer you got.

Log in to reply

Yeah, I solved it. My answer is 7.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

$\text{Doubt : 3}$

Uncertainty in position and momentum are equal. Then what will be the Uncertainty in velocity ?

Log in to reply

I don't think uncertainty in position and momentum are relativistically equal. However, if a non-relativistic assumption is to be made, then from Heisenberg's, and taking p=mv, then uncertainty in velocity>=(h/2pi)X(1/(uncertainty in position X mass)). Sorry for the math ambiguity. My device doesn't type LaTeX.

Log in to reply

Yes you are correct. You got the correct answer. Regarding the latex you can keep it in \ (...\ ).

Log in to reply

Log in to reply

$\text{Doubt : 4}$

In $(Si_4O_{12})^{8-}$, how many $Si - O - Si$ linkages are there ?

Log in to reply

I have an answer, but I am not totally sure it is correct. Coordination structure chemistry of silicates and silicones is my weakest point in chemistry. Perhaps I need to practise more!:)

Log in to reply

What is the answer bro?:)

Log in to reply

It is 4.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Thanks guys. Keep sending problems and lets discuss!

Log in to reply

Hi guys! For sure we all have noticed that the derivative of kinetic energy is momentum. Is there a physical explanation for this?

Log in to reply

Quantitatively speaking, momentum is the product of mass of a body and its velocity. It is denoted by $\overline{P}$. $\large \overline{P} = m \overline{v}$ But the above definition is valid only when velocity of the body is constant. If the velocity of the body is variable we cannot use this formula and we should go by calculus. Physically speaking,

momentum is the rate of change of kinetic energy with respect to its velocity. So, you ca say it askinetic energy at that instance. Here is how we get $\overline{P} = m \overline{v}$ from kinetic energy. $K.E = \dfrac12 m (\overline{v})^2$ Now, differentiate both side with respect to velocity. We get : $\dfrac{d}{dx} K.E = \dfrac{d}{dx} \left ( \dfrac12 m (\overline{v})^2 \right )$ As, we know $\dfrac{d}{dx} K.E = \overline{P}$, we get : $\overline{P} = \dfrac12 \cdot m \cdot 2 \overline{v}$ So, we get : $\large \boxed{\color{#3D99F6} \overline{P} = m \overline{v}}$Log in to reply

Perfect bro!

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Explain the Bohr theory of atoms, combining both mathematics and physics in your explanations.

Log in to reply

Does anyone know how to post a solution of a problem that doesn't have a posted solution yet?

Log in to reply

If you got it correct you click the button "No solution" under Continue and write. And if you got it wrong you can't.

Log in to reply

Thanks a lot, bro!

Log in to reply

Log in to reply

@Mohmmad Farhan why can't you come here. I think this is a best place for a student like you. You can post your quires here.

Log in to reply

Sorry! I am not really active these days because of exams

Log in to reply

Ok. No problem !!!

Log in to reply

How do I post numerical answer problems on Brilliant?

Log in to reply

I think you have posted many problems in brilliant. However, when you are writng a question there will be two options, either Number or Multiple choice. You can select whatever you wish.

Log in to reply

Gearing up for today's 1st round olympiads!

Log in to reply

Good luck!

Log in to reply

Thanks. The results will be uploaded online in about 1.5 hours. Meanwhile I am posting them here for our consumption. Solve some, post solutions and invite others to do same!

Log in to reply

Log in to reply

Log in to reply

Problem 1: A password consists of $4$ distinct digits such that their sum is $19$ and exactly two of its digits are prime, e.g. $0397$. How many possible such passwords exist?

Log in to reply

2,3: (2,3,6,8)

2,5: (2,5,4,8)

2,7: (2,7,4,6),(2,7,1,9)

3,5: x

3,7: (3,7,1,8),(3,7,0,9)

5,7: (5,7,1,6)

There are $7\times4!=168$ possibilities

Log in to reply

How did you get all possibilities?

Log in to reply

Log in to reply

Problem 2: What is the maximum possible area of a quadrilateral of sides $1, 4, 7, 8$?

Log in to reply

I think we should use the concept of maxima and minima.

Log in to reply

Perhaps you should solve it. I used the maximality condition of Bretschneider's formula. My answer was $18$.

Log in to reply

Log in to reply

Log in to reply

Looks similar to:

https://brilliant.org/problems/hexagon-octagon-in-a-rectangle/?ref_id=1538063

Maybe a harder version perhaps! :D

Log in to reply

Problem 3: $20$ lines are drawn in a plane. What is the maximum number of parts into which the plane can be divided by the $20$ straight lines?

Log in to reply

I think it is $211$

Log in to reply

There is a trick. First, take the 20th triangular number. $\displaystyle\frac{20(20+1)}{2} = 210$ Add 1. $210+1=211$ These numbers are known as pizza numbers and are always one more than a triangular number.

P.S. @EKENE FRANKLIN did you use this method?

Log in to reply

Great! Just what I wanted, and what I used during the examination!

Log in to reply

Log in to reply

What is the remainder when $1^{241} + 2^{241} + 3^{241} + 4^{241}$ is divided by $5$?

Log in to reply

$0$

Log in to reply

Of course that is the answer, but prove it.

Log in to reply

$1^{124}$ is obviously 1. Since the repetition in the last digit is (for 2): 2, 4, 8, 6 then $241 \div 4 = k (\text{Remainder}1$) the first number is 2 (in this set). Apply this to the other powers. Summing the last digits, we get 10 and $10 \div 5 = k (\text{Remainder}0)$

Since the divisibility rule of 5 only concerns the last digit, we have to find the last digits of the values.Log in to reply

Log in to reply

Log in to reply

Log in to reply

Problem 5: Find the general term of the sequence described by $a_n = 4a_{n - 1} - 3a_{n - 2}$ given that $a_1 = 1$ and $a_2 = 9$.

Log in to reply

$a_n=4\times3^{n-1}-3$

Log in to reply

Great. This was what I got. But do you mind showing your solution so I can clarify mine?

Log in to reply

$x^2=4x-3$ and get $x=3$ or $1$. Let $b_n=3^n-1^n$.

Solve the equationThe first few terms of $b_n$ is $2,8,26,80...$ and $b_n$ also satisfies the recursion $b_n=4b_{n-1}-3b_{n-2}$

Compare the two sequences: $a_n=\frac43b_n-\frac53=4\times3^{n-1}-3$

Log in to reply

Log in to reply

Log in to reply

Log in to reply

@X X I think this is your first problem of the week in easy catogery.

Log in to reply

Log in to reply

Number + Reciprocal will take me to 1 lakh (100 K) solvers. But it fell short of 7 K. But luckily this week too my question came in one of the problems of week (the first one) so it is confirmed that I will reach the milestone in one or two days.

But I am not fully done. I expected thatLog in to reply

Log in to reply

Log in to reply

Thundering Question) is the third one.

OH !!! Your problem is featured as the second one in the problems of the week. But my first problem (Log in to reply

Log in to reply

Log in to reply

Log in to reply

It's a Fact:I have made a hatrick in June 9 - June 29 (3 weeks) as 3 of my problem continuously came in easy part of the POTW. Now again the chance has come for me. Last week and this week too two of my problems are featured. So, if luck favors next week to I can have a problem in POTW. I am thinking very hard on which question should I post the next.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

here. It is posed by B.D

How is my new problem, check itLog in to reply

Log in to reply

Log in to reply

Log in to reply

I made the cut for the 2nd round! I scored $76.70$ out of a maximum possible 110. Hurray!

Log in to reply

Oh !!! Congrats.

Log in to reply

Thanks a lot. But no one apart from us is solving the problems. I want to check my solutions and my faulty areas. Please direct the problem solving masters of Brilliant here to help me out.

Log in to reply

Log in to reply

Hi guys !!! I want to tell you some secret. I think next week would be a week of physics. Because this week I have found six problems which have equal chances in coming to problems of the week. There are Rohit Gupta's Trick Spring Balance and Spring Balance, Pranshu Gaba's Three blocks Sliding and Relative Stuntmen Motion, Danielle Scarano's Thermographic Dog and my Mt. Everest vs Mt. Godwin Austin. I think these question will be featured definitely this week if not possible then next week.

Log in to reply

@Calvin Lin

Log in to reply

I think you there is some error in spelling or you have kept a gap between the symbol and name. Once check again. If it is correct then you should get it in blue color link and not just normal text.

For example you should type it as @ _ Ekene Franklin ( _ symbol means no gap) then you will get it as @EKENE FRANKLIN

Log in to reply

It is not still working. Do I need to add something like a code or anything, or should I just type it?

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

@Calvin Lin

Log in to reply

@Calvin Lin.

Log in to reply

@X X, @Michael Mendrin, @Chew-Seong Cheong, @Mohmmad Farhan,and the rest of all, Can you please participate in this message-board (as requested by Ekene Franklin)

Log in to reply

What courses would you recommend for a 4th grader like me?

Log in to reply

You are 4 the grade ????!!!!!

Log in to reply

10 years old. I told you

Log in to reply

Log in to reply

Log in to reply

I am going to be 5th grade

Log in to reply

Log in to reply

Log in to reply

My first trophy was in Grade 1(third)[english], Second in grade 2 (1st)[first scrabble competition] and third in grade 2(Best school player award)[first scrabble competiton]

Log in to reply

## BrilliantForLife

Dare you to toggle $\LaTeX$Log in to reply

I have a proof for the existence of infinite dimensions.

On a line (1 Dimension), a number can be represented by a point. On a grid (2 Dimensions), an intersection is represented for the data in a cell. In a cube (3 Dimensions), data can still be represented on a point (where straight lines intersect). Following this pattern, there are infinite dimensions (because there are $\aleph_0$ numbers).

Log in to reply

Problem 6: Find all primes which are the sum of two primes and difference of two primes.

Log in to reply

5=7-2=3+2,this is the only possibility.

Log in to reply

Exactly. Just what I did during the exam, using the logic that if a prime satisfies those conditions, then the only even prime, 2 must be in the sum and difference.

Log in to reply

Problem 7: Simplify $S = (cot 10^\circ - 3\sqrt{3})(cosec 20^\circ + 2cot 20^\circ)$

Log in to reply

Why are you keeping square brackets. For square root you just need to keep flower brackets.

Log in to reply

For trigonometric functions, logarithms, limts, etc you must keep a slash before them. Like \cot will be as $\cot$ and \log will be as $\log$.

Log in to reply

Problem 8: A unit square is completely covered by $3$ identical circles. Find the smallest possible diameter of the circles.

Log in to reply

Problem 9: How many $6$ digit numbers can be formed using only odd digits?

Log in to reply

Is it 5^6?

Log in to reply

Correct. Nice stuff. What did you do?

Log in to reply

Log in to reply

Log in to reply

DO YOU SERIOUSLY HAVE TO GIVE ME 46 NOTIFICATIONS OVERNIGHT!

Log in to reply

Is that bad, Mohmmad? I am usually on Brilliant throughout the night.

Log in to reply

I HAVE EXAMS

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Don't call me Mohmmad

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Did you know that :

$1 + \omega = \omega \ but \ \omega + 1 \neq \omega$

Freakin' cool right?

P.S. $\displaystyle \omega \ is \ the \ second \ lowest \ level \ of \ \infty \ after \ \aleph_0$

Log in to reply

Finally I reached it. I have reached

1 lakh (100 k)solvers in 91 problems.Log in to reply

Congratulations!

Log in to reply

Do you know the minimum people to reach?

Log in to reply

I didn't get your point !!! Are you asking about minimum people required to get contribution page.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Suppose lets say a man jumps from a building with initial velocity $u$. After $x$ seconds another man freely falls from the same building and from the same height. Now, we can say that the displacement of both the man's are equal as they both reach the ground simultaneously after they jump from same point, so we can equate their distances. Here is what I did : $ut + \dfrac12 gt^2 = \dfrac12 g(t - x)^2$ where $t$ is the time taken by the first person to reach the ground. The main part of my doubt is that whether we should write the time taken by second person as $(t - x)$ or $(t + x)$.

Log in to reply

Log in to reply

$x$ seconds his time period will be $(t - x)$ seconds. Let's ask it to staff.

What I think is that as the second person jumps afterLog in to reply

Log in to reply

Log in to reply

Log in to reply

$t-x$

Yes, I too think the time taken by the second person isLog in to reply

Log in to reply

DO or DIEYou are lost in a forest on a cold midnight day. The temperature is quite low and it is bitter cold. Now you have only two chances :

You should lie on the ground and should shrink your body like a tight pack.

Go and stay in the water in a pond nearby.

There not much time left. Take your decision before cold kills you. So,

what wold you choose?Log in to reply

First option.

Log in to reply

But the second one is the correct choice you have to make.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Hello to everyone! I have not been around for some time now on Brilliant. However, I met on my return a delightful change in the method of posting options for multiple choice questions on Brilliant. Kudos to Calvin Lin and the truly brilliant Brilliant team!

Log in to reply

Which questions would you handpick for people? (ie. Your favourite questions)