This is a question for Mr.Jon Haussmann.Just because you are not very active in the discussion forums I decided to ask you this in form of a note.Whenever I open a level 5 problem almost everyday I find your name in the recent solvers list and also you are always at the peak of the of the maximum points list per week.(not to mention per month and all-time)

How can you be such an efficient problem solver??Your problem solving skills are over the sun.So honestly you are one of the many people on Brilliant who inspire me to keep improving myself.Any suggestions on how to be as good as you are???

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TopNewestIf you want to improve at problem solving, the best way is to practice, and just try solving lots of problems.

To solve a problem efficiently, you have to conscientiously look for quick and simple ways. The problem "Directrix will Drive you Delirious" is a good example of this. You can write down the equations for a rotated parabola, but this takes a lot of time, and it's easy to make a calculation mistake.

Instead, you can realize that it's a lot easier to rotate a line than it is to rotate a parabola. Also, if you rotate a line around a point, then the distance from the point to the line stays the same. This means you can easily set up an equation using the formula for the distance between a point and a line. Neither of these is a particularly sophisticated idea; you just have to think about a way to approach the problem that will make it easiest for yourself.

Another good example is "Dice Sum 3". You can try writing down the combinations that work, or you can pull out tools like recursion or induction. But if you look at the problem the right way, the answer pops out easily. A lot of problems include some kind of "hook" that collapses the problem; you just have to look for it. As you gain experience in problem solving, it will get easier to see what kind of approaches will work on which problems.

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Do you recommend reading a lot of books on the topic alongside solving problems???

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Sure, there are a lot of great books out there on problem solving.

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Can you please elaborate on how to find the "hook" of a given problem ? Thanks.

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To find the hook, you have to look for it. That's not as obvious as it sounds.

As perhaps a simple example, take the problem "Number Theory or Algebra? Part 6". The problem is to find all \(p\) such that \(p\), \(p + 2\), and \(p + 4\) are all prime.

This looks a lot like the problem of whether there are an infinite number of twin primes, and this problem is unsolved. And given that there is no simple formula for primes, it means there

hasto be an easy way to solve the problem, because otherwise, it probably wouldn't be solvable at all. So when you tackle this problem, you should look specifically for the easy way, and not for a complicated argument.This approach does assume that (1) the problem posed is solvable, and (2) the problem has a simple solution. At the very least, these assumptions give you a place to start, and they work fairly well in practice, because people who propose problems tend to like these characteristics.

For example, if someone asked you to find all the twin primes less than 1000, that would not be a very interesting problem (at least to me); it would involve mostly a brute force calculation, with little insight. On the other hand, if someone asked you to find all \(p\) such that \(p\), \(p + 2\), and \(p + 4\) are all prime, that would be more interesting, precisely because it may look complicated, but it's actually quite simple.

So that's what I mean when I say that you have to look for simplicity.

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He's really impressive. He's always one of the first people to solve my problems (and often THE first one).

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Also quite often the ONLY one.

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Same.

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Same here.

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I'll tag you here @Jon Haussmann ....

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SERIOUSLY! Is there anything you CAN'T solve? Where did you learn? What competitions have you ACED?

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I certainly agree, I also found out that @Vishnuram Leonardodavinci aslo solves almost every level 5 problems

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Okay, I am at a loss at how @Jon Haussmann solved Quadratic System of Equations within 45 seconds of when I posted it... @Nathan Ding solved it before him only because he was my beta tester, but I never released the problem to anyone else.

Perhaps the problem I posted just happened to be a well-known problem that I did not know before?

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The rate at which he solves problems is really insane!

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How do you tag people ?

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First type @ and then type the name of the person(Only the first 2-3 letters and then a list will appear and you can choose the name you want.)

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Wolfram alpha maybe

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Jon wouldn't use Wolram Alpha... He's a legendary problem solver.

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I totally agree with you...hats off

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