Soft question- The Bashing Technique and Other powerful techniques for Olympiads












6












$begingroup$


I am relatively new to the Olympiad style maths problems and I find the word "bashing" being thrown around a lot in the community and I haven't really understood it. I do know about "co-ordinate bashing" using Barycentric co-ordinates and complex numbers but I've also seen people use the term "bashing" in Number Theory, Combinatorial and Algebraic questions and don't know why.



My Question- What does the term "bashing" generally mean in Mathematics(in the broader sense)?



Also, if anyone could provide me some other powerful problem solving tools like Bashing which are useful for Maths Olympiads I would be highly obliged. By "Problem Solving Tools" I refer to concepts like Inversive, Projective and Homothety in geometry;LTE and Chinese Remainder Theorem in Number Theory; Vieta Root Jumping in Algebra. I only know a few of these and would like to see a comprehensive list of all(or most) of such important techniques. Even a link would suffice.



Thanks in advance.(First question on Stack Exchange).






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  • 1




    $begingroup$
    Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
    $endgroup$
    – Blue
    15 hours ago
















6












$begingroup$


I am relatively new to the Olympiad style maths problems and I find the word "bashing" being thrown around a lot in the community and I haven't really understood it. I do know about "co-ordinate bashing" using Barycentric co-ordinates and complex numbers but I've also seen people use the term "bashing" in Number Theory, Combinatorial and Algebraic questions and don't know why.



My Question- What does the term "bashing" generally mean in Mathematics(in the broader sense)?



Also, if anyone could provide me some other powerful problem solving tools like Bashing which are useful for Maths Olympiads I would be highly obliged. By "Problem Solving Tools" I refer to concepts like Inversive, Projective and Homothety in geometry;LTE and Chinese Remainder Theorem in Number Theory; Vieta Root Jumping in Algebra. I only know a few of these and would like to see a comprehensive list of all(or most) of such important techniques. Even a link would suffice.



Thanks in advance.(First question on Stack Exchange).






contest-math problem-solving







share|cite|improve this question







New contributor




Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







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  • 1




    $begingroup$
    Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
    $endgroup$
    – Blue
    15 hours ago














6












6








6


1



$begingroup$


I am relatively new to the Olympiad style maths problems and I find the word "bashing" being thrown around a lot in the community and I haven't really understood it. I do know about "co-ordinate bashing" using Barycentric co-ordinates and complex numbers but I've also seen people use the term "bashing" in Number Theory, Combinatorial and Algebraic questions and don't know why.



My Question- What does the term "bashing" generally mean in Mathematics(in the broader sense)?



Also, if anyone could provide me some other powerful problem solving tools like Bashing which are useful for Maths Olympiads I would be highly obliged. By "Problem Solving Tools" I refer to concepts like Inversive, Projective and Homothety in geometry;LTE and Chinese Remainder Theorem in Number Theory; Vieta Root Jumping in Algebra. I only know a few of these and would like to see a comprehensive list of all(or most) of such important techniques. Even a link would suffice.



Thanks in advance.(First question on Stack Exchange).






contest-math problem-solving







share|cite|improve this question







New contributor




Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I am relatively new to the Olympiad style maths problems and I find the word "bashing" being thrown around a lot in the community and I haven't really understood it. I do know about "co-ordinate bashing" using Barycentric co-ordinates and complex numbers but I've also seen people use the term "bashing" in Number Theory, Combinatorial and Algebraic questions and don't know why.



My Question- What does the term "bashing" generally mean in Mathematics(in the broader sense)?



Also, if anyone could provide me some other powerful problem solving tools like Bashing which are useful for Maths Olympiads I would be highly obliged. By "Problem Solving Tools" I refer to concepts like Inversive, Projective and Homothety in geometry;LTE and Chinese Remainder Theorem in Number Theory; Vieta Root Jumping in Algebra. I only know a few of these and would like to see a comprehensive list of all(or most) of such important techniques. Even a link would suffice.



Thanks in advance.(First question on Stack Exchange).






contest-math problem-solving




contest-math problem-solving






share|cite|improve this question







New contributor




Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question







New contributor




Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question






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asked 16 hours ago









Anurag SahaAnurag Saha

334




334




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Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Anurag Saha is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    $begingroup$
    Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
    $endgroup$
    – Blue
    15 hours ago














  • 1




    $begingroup$
    Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
    $endgroup$
    – Blue
    15 hours ago








1




1




$begingroup$
Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
$endgroup$
– Blue
15 hours ago




$begingroup$
Clarification of the term "bashing", and a request for additional problem-solving tools, should probably be separate questions.
$endgroup$
– Blue
15 hours ago










3 Answers
3






active

oldest

votes


















7












$begingroup$

"Bashing" is a term for brute force methods, applied with very little cleverness. These are looked down on in contest mathematics, both because they aren't "pretty" and because they tend to take more time and computational effort than is practical in a live contest.



How do you tell if a solution is "bashing"? That's an entirely subjective judgment. The more you like it, the less likely you are to call it bashing.



What's the advantage of methods that might get called bashing? Reliability. Often, that method is something you know will work if you put enough time and effort into it. For example, consider the two top-rated answers to this recently active inequality problem; one is a short and sweet application of a classical inequality to eliminate the square roots, while the other is a very long slog of multivariable calculus and numerical root-finding, finding all twenty critical points of a function in order to find its minimum. The latter is certainly fairly bashy - I might not have gone through with it if I had realized how much work it was from the start - but it's also a complete solution, where the former isn't. After the simplification, that attempt stalls out with no clear next step.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
    $endgroup$
    – Mast
    8 hours ago



















4












$begingroup$

I think in general the term bashing is used to describe an approach which is about applying a small set of manipulations over and over until you get an answer. These approaches usually don't require much insight.



One other trait of bashing which I can think of is that it is often very computational. This will usually go hand in hand with bashing's non-insightfulness.



The example you gave of using coordinate geometry to solve geo problems is a prime example of bashing as it is just a bunch of messy algebra after you translate the terms of the problem to coordinate geometry.






share|cite|improve this answer









$endgroup$





















    2












    $begingroup$

    In inequalities examples of bashing they are:




    1. Buffalo Way. See here: https://artofproblemsolving.com/community/c6h522084


    2. uvw . See here: https://artofproblemsolving.com/community/c6h278791







    share|cite|improve this answer









    $endgroup$













      Your Answer





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      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      7












      $begingroup$

      "Bashing" is a term for brute force methods, applied with very little cleverness. These are looked down on in contest mathematics, both because they aren't "pretty" and because they tend to take more time and computational effort than is practical in a live contest.



      How do you tell if a solution is "bashing"? That's an entirely subjective judgment. The more you like it, the less likely you are to call it bashing.



      What's the advantage of methods that might get called bashing? Reliability. Often, that method is something you know will work if you put enough time and effort into it. For example, consider the two top-rated answers to this recently active inequality problem; one is a short and sweet application of a classical inequality to eliminate the square roots, while the other is a very long slog of multivariable calculus and numerical root-finding, finding all twenty critical points of a function in order to find its minimum. The latter is certainly fairly bashy - I might not have gone through with it if I had realized how much work it was from the start - but it's also a complete solution, where the former isn't. After the simplification, that attempt stalls out with no clear next step.






      share|cite|improve this answer









      $endgroup$













      • $begingroup$
        This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
        $endgroup$
        – Mast
        8 hours ago
















      7












      $begingroup$

      "Bashing" is a term for brute force methods, applied with very little cleverness. These are looked down on in contest mathematics, both because they aren't "pretty" and because they tend to take more time and computational effort than is practical in a live contest.



      How do you tell if a solution is "bashing"? That's an entirely subjective judgment. The more you like it, the less likely you are to call it bashing.



      What's the advantage of methods that might get called bashing? Reliability. Often, that method is something you know will work if you put enough time and effort into it. For example, consider the two top-rated answers to this recently active inequality problem; one is a short and sweet application of a classical inequality to eliminate the square roots, while the other is a very long slog of multivariable calculus and numerical root-finding, finding all twenty critical points of a function in order to find its minimum. The latter is certainly fairly bashy - I might not have gone through with it if I had realized how much work it was from the start - but it's also a complete solution, where the former isn't. After the simplification, that attempt stalls out with no clear next step.






      share|cite|improve this answer









      $endgroup$













      • $begingroup$
        This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
        $endgroup$
        – Mast
        8 hours ago














      7












      7








      7





      $begingroup$

      "Bashing" is a term for brute force methods, applied with very little cleverness. These are looked down on in contest mathematics, both because they aren't "pretty" and because they tend to take more time and computational effort than is practical in a live contest.



      How do you tell if a solution is "bashing"? That's an entirely subjective judgment. The more you like it, the less likely you are to call it bashing.



      What's the advantage of methods that might get called bashing? Reliability. Often, that method is something you know will work if you put enough time and effort into it. For example, consider the two top-rated answers to this recently active inequality problem; one is a short and sweet application of a classical inequality to eliminate the square roots, while the other is a very long slog of multivariable calculus and numerical root-finding, finding all twenty critical points of a function in order to find its minimum. The latter is certainly fairly bashy - I might not have gone through with it if I had realized how much work it was from the start - but it's also a complete solution, where the former isn't. After the simplification, that attempt stalls out with no clear next step.






      share|cite|improve this answer









      $endgroup$



      "Bashing" is a term for brute force methods, applied with very little cleverness. These are looked down on in contest mathematics, both because they aren't "pretty" and because they tend to take more time and computational effort than is practical in a live contest.



      How do you tell if a solution is "bashing"? That's an entirely subjective judgment. The more you like it, the less likely you are to call it bashing.



      What's the advantage of methods that might get called bashing? Reliability. Often, that method is something you know will work if you put enough time and effort into it. For example, consider the two top-rated answers to this recently active inequality problem; one is a short and sweet application of a classical inequality to eliminate the square roots, while the other is a very long slog of multivariable calculus and numerical root-finding, finding all twenty critical points of a function in order to find its minimum. The latter is certainly fairly bashy - I might not have gone through with it if I had realized how much work it was from the start - but it's also a complete solution, where the former isn't. After the simplification, that attempt stalls out with no clear next step.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered 15 hours ago









      jmerryjmerry

      12k1628




      12k1628












      • $begingroup$
        This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
        $endgroup$
        – Mast
        8 hours ago


















      • $begingroup$
        This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
        $endgroup$
        – Mast
        8 hours ago
















      $begingroup$
      This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
      $endgroup$
      – Mast
      8 hours ago




      $begingroup$
      This isn't exclusively used in mathematics either. If you're driving a nail into a piece of wood with anything except for a hammer or naildriver, you're bashing it in. It's a common term for brute-forcing anything with whatever tools you got on hand, instead of doing it the right way. Except for those cases where bashing is the only right way, of-course.
      $endgroup$
      – Mast
      8 hours ago











      4












      $begingroup$

      I think in general the term bashing is used to describe an approach which is about applying a small set of manipulations over and over until you get an answer. These approaches usually don't require much insight.



      One other trait of bashing which I can think of is that it is often very computational. This will usually go hand in hand with bashing's non-insightfulness.



      The example you gave of using coordinate geometry to solve geo problems is a prime example of bashing as it is just a bunch of messy algebra after you translate the terms of the problem to coordinate geometry.






      share|cite|improve this answer









      $endgroup$


















        4












        $begingroup$

        I think in general the term bashing is used to describe an approach which is about applying a small set of manipulations over and over until you get an answer. These approaches usually don't require much insight.



        One other trait of bashing which I can think of is that it is often very computational. This will usually go hand in hand with bashing's non-insightfulness.



        The example you gave of using coordinate geometry to solve geo problems is a prime example of bashing as it is just a bunch of messy algebra after you translate the terms of the problem to coordinate geometry.






        share|cite|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          I think in general the term bashing is used to describe an approach which is about applying a small set of manipulations over and over until you get an answer. These approaches usually don't require much insight.



          One other trait of bashing which I can think of is that it is often very computational. This will usually go hand in hand with bashing's non-insightfulness.



          The example you gave of using coordinate geometry to solve geo problems is a prime example of bashing as it is just a bunch of messy algebra after you translate the terms of the problem to coordinate geometry.






          share|cite|improve this answer









          $endgroup$



          I think in general the term bashing is used to describe an approach which is about applying a small set of manipulations over and over until you get an answer. These approaches usually don't require much insight.



          One other trait of bashing which I can think of is that it is often very computational. This will usually go hand in hand with bashing's non-insightfulness.



          The example you gave of using coordinate geometry to solve geo problems is a prime example of bashing as it is just a bunch of messy algebra after you translate the terms of the problem to coordinate geometry.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 16 hours ago









          Isaac BrowneIsaac Browne

          4,85241234




          4,85241234























              2












              $begingroup$

              In inequalities examples of bashing they are:




              1. Buffalo Way. See here: https://artofproblemsolving.com/community/c6h522084


              2. uvw . See here: https://artofproblemsolving.com/community/c6h278791







              share|cite|improve this answer









              $endgroup$


















                2












                $begingroup$

                In inequalities examples of bashing they are:




                1. Buffalo Way. See here: https://artofproblemsolving.com/community/c6h522084


                2. uvw . See here: https://artofproblemsolving.com/community/c6h278791







                share|cite|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  In inequalities examples of bashing they are:




                  1. Buffalo Way. See here: https://artofproblemsolving.com/community/c6h522084


                  2. uvw . See here: https://artofproblemsolving.com/community/c6h278791







                  share|cite|improve this answer









                  $endgroup$



                  In inequalities examples of bashing they are:




                  1. Buffalo Way. See here: https://artofproblemsolving.com/community/c6h522084


                  2. uvw . See here: https://artofproblemsolving.com/community/c6h278791








                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 16 hours ago









                  Michael RozenbergMichael Rozenberg

                  106k1894198




                  106k1894198






















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