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.

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'Notre Dame' is originally from French and when translated to English, it means "Our Lady". It is a reference to Mary, the mother of Jesus. The school [or college as it is called here] was founded by the Congregation of the Holy Cross.

The school is very strict about discipline and attendance is 100% compulsory. This part is from Wikipedia:

Notre Dame College gained reputation of the best institution for higher secondary education in the country. The highest number of perfect GPA holders in national examination (H.S.C.) and the exceptional success of its students in university admission tests bear testimony to this.

On the downside, they put too much pressure on you and there's a ton of homework everyday. The school website always seems to be unavailable.

Ah, I was thinking of that you got into Notre Dame in US. Didn't know that "Notre Dame" meant "My Lady", and that there are several higher education institutions with Notre Dame in their name.

HAHAHAHAHA! Yes... It's quite hard to do! You click on one person, then you click on another, then you click on another, etc.. It's MUCH harder than being followed by 3000 people! Totally... (sarcastic face). :D

@Anish Puthuraya So you're a fan of Linkin Park? What is your favorite song by them? What is your favorite album? Have you heard their new new song "Guilty All The Same" from their upcoming album "The Hunting Party"?

@Mursalin Habib
–
Oh, really? I need to update that then. It's been a really long time since I took a look at that. I'm curious - did you have the willpower to read my entire post on the beauty of mathematics?

@Trevor B.
–
I loved reading it. I like reading other people's profiles when I'm bored.

When was the last time you updated your profile? Because I'm pretty sure there was some mention of Bob Krueger there somewhere [just curious, that's all].

@Mursalin Habib
–
I think I updated it about two or three months ago.

When I was doing my science fair project, I needed to learn relatively advanced Python in a week, so I asked for some help with the code. He provided a sample code that I used in the project to get second at the county science fair, and I made a mental promise to pay him back by learning Python. The rest is history.

@Rubayet Tusher , congratulations on leveling up in algebra! I see that you are maintaining your streak for the last couple of days. Why don't you post a problem so that others can give it a shot? And you should seriously consider following some more people.

I was doing the Australian Maths Competition, not the American Maths Competition. It was way easier than I thought it would be. My favourite question probably was the last question.

What is largest 3 digit number such that it is equal to the sum of its hundreds digit, the square of its tens digit and the cube of the units digit?

I am pretty sure I was the only boy in the classroom to get that question (we had female teachers who also did the test as a practice of their skill).

Victor Loh was also participating in this so you can ask him as well.

@Mursalin Habib
–
Hmm, yes. I first eliminated the cases for the first digit and last digit. This greatly reduced the number. Then, because I didn't want to get it wrong, I used trial and error to determine the answer.

@Tahsin Ahmed You said that you are not a big fan of the MCQ system. Did you try out this set of problems? These problems wouldn't work without the MCQ format and the solutions require proving something as opposed to finding a numerical answer. Let me know what you think of them.

@Peter Taylor , do I qualify as a person who's worthy of being featured i your "cool people's message boards!" set? :)

By the way, although people can't directly re-share this note, there is a way to re-share this. If you like it, it goes to your "liked" feed and it is re-shareable from there. Are there any plans to fix this [It's really not that important but I'm just putting it out there.]?

Let me know if other cool people are making message boards, and I'll add them.

Re: the "hacky reshareability of notes published directly to sets" I will add it to our cue of bugs/minor inconsistencies. We will fix it when all other things of higher priority have been fixed(which could be a very long time). E.g. when ever presented with decisions about how to spend our time like "make the website faster" or "block resharing of notes that were published directly to sets" we are always going to go for things that affect more people. Thanks for bringing it up though!

@Mursalin Habib It says in your profile that you like reading webcomics. My favorite is Homestuck, by Andrew Hussie, and I have included characters from it in a couple of problems (like this one) off of it. Have you heard of it?

If you want to check out Homestuck, you should probably know that it is really long (almost 6000 pages and counting). It seems really pointless at the beginning, but everything in the beginning will make sense later on. And lastly, know that when you get past all of the weird stuff that happens in it, there lies a really interesting commentary under the surface. Basically, if you're patient enough to read it and you don't mind reading about some really weird characters and events, the hours you spend reading it will be well worth it when you finish.

But if you don't like it, that's fine. Lots of people can't get over the fact that the first 500 pages or so (the pages are really short, sometimes) can basically be summarized by "No one can find any of their belongings."

@Abba F , welcome to Brilliant! If you're looking for problems of a specific level, use the search bar. Search for "." [the period symbol] and filter topics, tags and levels. You should also consider following more people if you want to see more stuff appear in your feed. Have you seen this?

Thanks! I've only been here a couple of days, so it's nice to get some pointers on the infrastructure. I've already found some very interesting sets through Who To Follow.

@Blake Mitchell , welcome to Brilliant! You should consider following some more people if you want more things in your feed. The search bar is a great way to find a lot of great problems and notes. If you search for "." [the period symbol], you practically pull up everything. Then you can use different filters for problems, sets, topics and levels of difficulties. Enjoy!

Your Wiki - Diophantine Equations - Solve by Factoring

In the first example can you please show a proof if a number prime factorization is $a^bc^de^f$ then it will have (b+1)(e+1)(f+1) divisors , I am not getting it

@Rahul Saha: I see that you've contributed to the functional equation introduction wiki. Could you clean it up a little bit, fix some of the typos and improve the format?

I can't seem to find any typos.Maybe someone else edited it.And can you please elaborate on how the format can be improved? I will be happy to make any improvements.

Needed some answer about problem posting rules and their rating system . I've already mailed @Calvin Lin, but didn't get any reply yet. Is there any post on this topic? Would really be helpful if I get the link.

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

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TopNewest@Fahim Shahriar Shakkhor , nice job being the only person to finish "I Don't Have A Name For This Yet!". Did you like the problems? Which one seemed the hardest to you?

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Pie? and Answer Very Carefully! bothered me much.

I assumed $\pi+e$ to be rational and I almost forgot $0$ is rational. They were really good ones.

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I noticed that your school is Notre Dame College. What's that about?

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'Notre Dame' is originally from French and when translated to English, it means "Our Lady". It is a reference to Mary, the mother of Jesus. The school [or college as it is called here] was founded by the Congregation of the Holy Cross.

The school is very strict about discipline and attendance is 100% compulsory. This part is from Wikipedia:

On the downside, they put too much pressure on you and there's a ton of homework everyday. The school website always seems to be unavailable.

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Ah, I was thinking of that you got into Notre Dame in US. Didn't know that "Notre Dame" meant "My Lady", and that there are several higher education institutions with Notre Dame in their name.

Time to revisit Duolingo to learn French :)

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@Finn Hulse , congratulations on following 3000 people! :) That is an incredible achievement!

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HAHAHAHAHA! Yes... It's quite hard to do! You click on one person, then you click on another, then you click on another, etc.. It's MUCH harder than being followed by 3000 people! Totally... (sarcastic face). :D

Log in to reply

@Anish Puthuraya So you're a fan of Linkin Park? What is your favorite song by them? What is your favorite album? Have you heard their new new song "Guilty All The Same" from their upcoming album "The Hunting Party"?

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Ive heard that song. They have come back to Rock music after quite a while.

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So your favorites?

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@Trevor B. Here's your favorite joke with a new twist.

There are 10 types of people in this world.

1) Those who don't know binary.

2) Those who expected the 10 to be in binary.

3) Those who expected the 10 to be in ternary.

4) Those who expected the 10 to be in quaternary.

5) Those who expected the 10 to be in quinary.

6) Those who expected the 10 to be in senary.

7) Those who expected the 10 to be in septenary.

8) Those who expected the 10 to be in octal.

9) Those who expected the 10 to be in nonary.

10) Normal people.

[This joke assumes that normal people know binary and there is no intersection between 1 and 10 :)]

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Haha, thanks for this! My favorite is the doctor, physicist, and statistician going hunting.

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I was actually going through people's profiles and read that this was your favorite math joke.

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When was the last time you updated your profile? Because I'm pretty sure there was some mention of Bob Krueger there somewhere [just curious, that's all].

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When I was doing my science fair project, I needed to learn relatively advanced Python in a week, so I asked for some help with the code. He provided a sample code that I used in the project to get second at the county science fair, and I made a mental promise to pay him back by learning Python. The rest is history.

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Here's a trick question that I came up with myself.

What is $1+1?$ Base $10,$ no tricks! $10,$ because the entire question was in base $2.$

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On a related note,

alt text

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@Cody Johnson , I ask this because I'm curious but who is [or was] Oscar Harmon?

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@Rubayet Tusher , congratulations on leveling up in algebra! I see that you are maintaining your streak for the last couple of days. Why don't you post a problem so that others can give it a shot? And you should seriously consider following some more people.

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@Sharky Kesa , how did the AMC go? Do you have a favorite problem?

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I was doing the Australian Maths Competition, not the American Maths Competition. It was way easier than I thought it would be. My favourite question probably was the last question.

What is largest 3 digit number such that it is equal to the sum of its hundreds digit, the square of its tens digit and the cube of the units digit?

I am pretty sure I was the only boy in the classroom to get that question (we had female teachers who also did the test as a practice of their skill).

Victor Loh was also participating in this so you can ask him as well.

Log in to reply

How did you approach the problem?

If you look at it, there aren't many cases to consider. Even a brute force approach shouldn't take much time.

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Now that the HSC results have come out, what have you decided to study as an undergrad?

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@Daniel Liu , can you post a solution to Classic Climbing Problem 2? It's driving me crazy!

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@Tahsin Ahmed You said that you are not a big fan of the MCQ system. Did you try out this set of problems? These problems wouldn't work without the MCQ format and the solutions require proving something as opposed to finding a numerical answer. Let me know what you think of them.

Log in to reply

@Peter Taylor , do I qualify as a person who's worthy of being featured i your "cool people's message boards!" set? :)

By the way, although people can't directly re-share this note, there

isa way to re-share this. If you like it, it goes to your "liked" feed and it is re-shareable from there. Are there any plans to fix this [It's really not that important but I'm just putting it out there.]?Log in to reply

It was so woefully incomplete without you :)

Let me know if other cool people are making message boards, and I'll add them.

Re: the "hacky reshareability of notes published directly to sets" I will add it to our cue of bugs/minor inconsistencies. We will fix it when all other things of higher priority have been fixed(which could be a very long time). E.g. when ever presented with decisions about how to spend our time like "make the website faster" or "block resharing of notes that were published directly to sets" we are always going to go for things that affect more people. Thanks for bringing it up though!

Log in to reply

@Mursalin Habib It says in your profile that you like reading webcomics. My favorite is Homestuck, by Andrew Hussie, and I have included characters from it in a couple of problems (like this one) off of it. Have you heard of it?

Log in to reply

I haven't heard of it, sorry. I'll be sure to check it out!

I like xkcd, spikedmath, abstrusegoose, zenpencils and cyanide and happiness to name a few.

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Ah, I enjoy Cyanide and Happiness as well.

If you want to check out Homestuck, you should probably know that it is really long (almost 6000 pages and counting). It seems really pointless at the beginning, but everything in the beginning will make sense later on. And lastly, know that when you get past all of the weird stuff that happens in it, there lies a really interesting commentary under the surface. Basically, if you're patient enough to read it and you don't mind reading about some really weird characters and events, the hours you spend reading it will be well worth it when you finish.

But if you don't like it, that's fine. Lots of people can't get over the fact that the first 500 pages or so (the pages are really short, sometimes) can basically be summarized by "No one can find any of their belongings."

I hope you like it!

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@Daniel Liu , you're going to destroy the JMO! The problems don't seem that hard. Good luck!

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@josh silverman , did you know that both of us co-incidentally have the same status? What are the odds! :)

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@Mayank Holmes , I think your chemistry problems are great! Would you please add a solution to this one?

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@Abba F , welcome to Brilliant! If you're looking for problems of a specific level, use the search bar. Search for "." [the period symbol] and filter topics, tags and levels. You should also consider following more people if you want to see more stuff appear in your feed. Have you seen this?

Log in to reply

Thanks! I've only been here a couple of days, so it's nice to get some pointers on the infrastructure. I've already found some very interesting sets through Who To Follow.

Log in to reply

@Blake Mitchell , welcome to Brilliant! You should consider following some more people if you want more things in your feed. The search bar is a great way to find a lot of great problems and notes. If you search for "." [the period symbol], you practically pull up everything. Then you can use different filters for problems, sets, topics and levels of difficulties. Enjoy!

Log in to reply

@Mursalin Habib Is there any hope of another MCQ set like the "Not As Easy As [1], [2], [3]" set? I really enjoyed it.

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I don't see why not.

However at this exact moment I do not have enough ideas for an entire set. Give it a week.

I'm really glad that you enjoyed the sets.

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@Daniel Lim , are you sure the answer to your problem, "Three Cows" is correct?

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I do believe that the answer is incorrect.

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It's wrong. Gonna change it. Really careless mistake.

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This is so embarrassing. This is what I got.

$\frac{1}{20}+\frac{1}{30}+\frac{1}{60}=\frac{6}{60}=\frac{1}{6}$

What have I done?

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Your Wiki - Diophantine Equations - Solve by Factoring

In the first example can you please show a proof if a number prime factorization is $a^bc^de^f$ then it will have (b+1)(e+1)(f+1) divisors , I am not getting it

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Read this.

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@Rahul Saha: I see that you've contributed to the functional equation introduction wiki. Could you clean it up a little bit, fix some of the typos and improve the format?

Thanks!

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I can't seem to find any typos.Maybe someone else edited it.And can you please elaborate on how the format can be improved? I will be happy to make any improvements.

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Hi :)

I just realized that I have never talked with you ! (other than some small comments here and there)

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@MD Omur Faruque , I'm on Facebook.

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I'm glad to know you are a moderator.

Needed some answer about problem posting rules and their rating system . I've already mailed @Calvin Lin, but didn't get any reply yet. Is there any post on this topic? Would really be helpful if I get the link.

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Head on to Brilliant chat and you can ask Calvin yourself.

This page should be able to answer some of the questions that you have.

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