What is your basic strategy to solve a "Brilliant" problem?

I am talking specially about maths problems....., those of a little bit higher difficulty level.

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
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

For me, the key is always "What does this problem mean? How can I make it fit a pattern that I know?" If the answer doesn't come to me quickly, I'll draw pictures (for geometry), or work random examples (for integer problems or functions), or twiddle with it until I can say "Ah-hah. This is a blodget."

Then I just solve it with the rule for blodgets. A trivial way of expressing it, but I think that the first question is always, always "What kind of problem is this? What tool should I use to solve it?"

Peter Lynn - 7 years, 12 months ago

i agree totally with Peter sir..... think over the questions what they are asking.... and think over the concepts you know related to the prob... and when you can co-relate you'll definitely be able to say Eureka :)

A Former Brilliant Member - 7 years, 12 months ago

My problem is to always find a way to mechanically solve the problem using programing...for example: all maths problems concerning find the least positive integer for certain functions and things, these type of problems literally crack when confronted with programing...thus I level up very quickly :)

Rajarshi Banerjee - 7 years, 12 months ago

The point is that the questions posed by brilliant don't require programming. Of course, you can brute force the question to arrive at your integer answer. Brilliant aims at furnishing and nourishing our problem-solving skills(solving problems without using any sort of help). It is true that all problems can be solved using a pen and paper. You really don't need computers and other sophisticated software's, equipment,etc, to solve any of the problems. I'd not be surprised to see a decline in the number of users of brilliant if the staff decides to take down their "Points Exchange" system.

I am not saying that you are wrong, but if you are an avid programmer you should look up for programming challenges on other websites(I'm sure there are many). Leveling up without actually understanding the elegant technique is not what brilliant wants from its students.

Aditya Parson - 7 years, 12 months ago

fully agreed with Aditya :)

A Former Brilliant Member - 7 years, 12 months ago

What makes you think I am doing it for points??? I am just trying to prove to the world...well mainly myself that mathematics is a powerful tool, but it has a saturation point, on the other hand if we use computer science with Mathematics we can not only access its full potential, but also simplify the problem....ask your-self would Newton have ever come up with Integral calculus if he knew how to find the area of a equation using co-ordinate geometry combined with the power of computing. See I am not against conventional mathematics, I just want to restore its simplicity where it possible to provide a more simpler outlook....this is the philosophy I believe in and that is why I do it ( well and because my college doesn't start till next month)

Rajarshi Banerjee - 7 years, 12 months ago

@Rajarshi Banerjee – I never said explicitly that "you" play for points. It was more general if not anything else. Also, I said that you are not wrong(Nobody is actually, at least in some way). I also think that "simple and complicated" is a subjective matter, and I usually try to not classify stuff into different categories.

Aditya Parson - 7 years, 12 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$