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Some easy unsolved math problems (High school grade)

  1. Jun 4, 2010 #1
    Hi, I'm currently studying in high school. What I often find are complicated math unsolved problems which require quite deep math knowledge that is not really taught at my gymnasium.
    Are there any open problems which fit me?

    I know some easy problems such as: Is there any odd perfect number? Is 10 a friendly number?...
    I'm much more interested in algebra, geometry, calculus and trigonometry than numbers alone.
    I like finding a way/method using math symbols, I need problems which do not require big-number calculations.

    Thanks for help...
  2. jcsd
  3. Jun 4, 2010 #2
    what makes you think those two questions are easy?
  4. Jun 4, 2010 #3
    By 'easy' I mean that it's easy to understand the question. For instance, I know what a perfect number is, so "is there any odd perfect number" question is understood by me.
  5. Jun 4, 2010 #4
  6. Jun 4, 2010 #5
    Most of these unsolved problems have been studied for a while and as a result, mathematicians have developed complicated tools and abstractions to helps them with these problems. The modern student would build a foundation studying things like abstract algebra and analysis - building your knowledge of decades of math while also building your problem solving skills - so that you can study these problems later. This is not to discourage you from finding an odd perfect number, but it may take some time.

    I would suggest going through Putnam (math competition) style problems if you are looking for a challenge at problem solving.
  7. Jun 4, 2010 #6
    Here's a one that's a bit physics and a bit maths but maybe too easy.
    1/R=1/R1 +1/R2 for parallel resistors.
    How do you produce examples of this with whole number values only?
    e.g. R1=14, R2=35 giving R=10.
    R1=21, R2=28, R=24 gives exactly R=8.
    R1=1400, R2=2600 produces 910 ohms.
  8. Jun 4, 2010 #7
    Last edited by a moderator: Apr 25, 2017
  9. Jun 4, 2010 #8
    You engineers will be the death of mathematical exactitude!
    R1=25461230 ohms
    R2=25375670 ohms
    In parallel R(total)=12709189 ohms (exactly)!
  10. Jun 4, 2010 #9
    Stan Ulam
    "pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points" :smile:
  11. Jun 4, 2010 #10
    Hi Atran, this problem doesn't require algebra, geometry, calculus or trigonometry. It is only arithmetic! So get a pencil out and a scrap of paper. Here's another example...
    R1=10553063310 ohms
    R2=154064581051 ohms
    R (total) is still a whole number.
  12. Jun 4, 2010 #11
    In reply to Xitami, Georg Ohm did okay out of the mathematical approach. It took Bavaria a while to realise it though. Stan Ulam is impressive too though! As is Stanisław Lem, an idea: explosive!!!
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