Competitive math players -- How do they solve so fast?

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Almost like muscle memory.1. Know your basic multiplication tables by heart, including squares and cubes. This will help you solve problems quickly without having to calculate each time.2. Practice is key. The more you practice, the more you will be able to recognize patterns and solve problems faster.3. Competitive math is like a game of Rubik's cube, where competitors have memorized different problem-solving strategies and can apply them quickly.4. The key to fast problem solving is to have a good foundation of knowledge and to practice solving various situations.5. Memorizing different problem-solving methods and techniques is similar to memorizing multiplication tables, but for more advanced problems.6. It's important to have a good understanding of basic math concepts in
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Hi, I have watched some videos of Raytheon Mathcounts Competitions and the likes on Youtube recently. I was awe struck by the shear speed that some of the players were able to solve the problems.

Some, so fast that I don't believe a human brain could actually properly solve if given to randomly with no prior experience related to that specific problem while only equipped with the foundational knowledge to solve such problems.

The players at various points blurted out correct answers within seconds before the question could even be fully read. I believe this must be like Rubiks cube competitive solvers where they have practiced so many possible situations and have memorized them into almost like the brains version of muscle memory with the solution or precise way to solve them ready at a moments notice.

The only way I can think of it is like students memorising squares, cubes and multiplicative tables that they can give off at a moments notice, except they are instead memorising outpoints and methods to more advanced problems.

Am I approximately correct in my hypothesis? I just don't know any other way they could solve so quickly. I have never engaged in competitive mathematics at any point in my life so forgive me if the answer is pretty obvious/trivial.
 
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Practice. Usually there is not much to calculate if you recognize how to do it.
You certainly want to know some basic results by heart, but you don't need many. Square numbers below 100, cubes of 2, 3, 4, 5 - things like that.

Spoilers:
  • For the first question it is sufficient to know that 50% is 1/2. Then technically you divide 3 by 1/2, but that is clearly 3*2=6, a trivial multiplication.
  • The n! answer came really quick, but again you don't have to actually calculate anything. n!/(n-1)! will give the factor n for the numerator and n!/(n+1)! will give the factor n+1 for the denominator. You just have to make sure you don't mess up the +1 (in other words: 8 is not the right answer). It helps if you encountered a similar expression before, but they do pop up once in a while in mathematics.
  • Juice: Volume scales with the height cubed, 2/3 of the height is left, so 8/27 of the volume is left. You should certainly know these cubes. Here comes the first actual calculation: 1 - 8/27 = 19/27 because 27-8=19.
  • 13/(p2-3): This one is a bit trickier. 13 is a prime, so the denominator can only be 1 or 13. A denominator of 1 means p2=4 or p=2, and a denominator of 13 means p2=16 or p=4. Sum: 2+4=6.
  • The cube root of 97336: There are tricks to calculate this very fast, but if you don't know them: 50^3 = 125000 which is a bit too large, but 40^3 = 64000 is too low. The result has to be somewhere around 45. The cube is even so the base number has to be even as well. If you cube 44 then the number ends with 4 (as 4^3=64 ends in 4), if you cube 46 the number ends in 6 as powers of 6 always do, if you cube 8 you get whatever but not 6, and 48 looks too large anyway. The answer has to be 46. You can find this faster than it is to type all this.
  • (x^2+2x+1)/(x^2+6x+9)=36/49: This needs some time and it doesn't surprise me the early answer was wrong. 36 and 49 are both squares, but they don't equal the numerator and denominator. You can recognize them as (x+1)^2 and (x+3)^2, then you can take the square root on both sides: (x+1)/(x+3)=6/7. The difference between numerator and denominator on the left side is twice as large, so let's expand the right side by 2 to match it: (x+1)/(x+3)=12/14 - okay that works, x=11.
Edit: Some more. All these can be solved faster than writing down the solution path.
 
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FAQ: Competitive math players -- How do they solve so fast?

1. How do competitive math players develop their speed in solving problems?

Competitive math players develop their speed through constant practice and exposure to different types of math problems. They also use strategies such as mental math techniques, breaking down problems into smaller parts, and utilizing shortcuts and patterns.

2. Do competitive math players have a natural talent for solving math problems quickly?

While some individuals may have a natural aptitude for mathematics, the speed at which competitive math players solve problems is largely a result of hard work and practice. With dedication and perseverance, anyone can improve their speed in solving math problems.

3. What kind of math problems do competitive math players typically solve?

Competitive math players are often faced with a wide range of math problems, including algebra, geometry, number theory, and combinatorics. They are also skilled in solving problems that require creative and critical thinking.

4. How do competitive math players stay calm and focused under pressure during competitions?

Competitive math players often have a strong ability to manage stress and maintain focus during competitions. This is usually a result of their extensive training and practice, as well as their ability to quickly identify and solve problems without getting overwhelmed by the pressure of the competition.

5. Can anyone become a competitive math player or is it only for a select few?

Anyone can become a competitive math player with the right attitude, dedication, and practice. While some individuals may have a natural inclination towards math, the majority of competitive math players have honed their skills through hard work and perseverance.

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