Let's play tag!

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP












4












$begingroup$


I have a short and bitter-sweet riddle for the community this evening. As always, I hope you enjoy it; good luck!




I want to play a game of tag; however, there are some very important rules:



  • We both start at the same point.

    • You cannot tag until the third turn or greater.


  • Each turn you take one step.

  • Each turn I double the number of steps I take.

    • Our stride is exactly the same.


  • We travel in a straight line.

  • We both take one initial step.

  • Our game is played on an infinitely flat plane

  • All steps are forwards, never backwards.

    • Assume we are infinitely traveling in a straight line.



Can you tag me?




Please explain your answer.



Hint:




Your step is on top, mine on bottom. Please note the math tag.

$frac11, frac12, frac14, frac18, frac116, frac132...$











share|improve this question











$endgroup$







  • 1




    $begingroup$
    Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
    $endgroup$
    – Krad Cigol
    Feb 10 at 3:09










  • $begingroup$
    @KradCigol I've updated my post to clarify this question and another.
    $endgroup$
    – PerpetualJ
    Feb 10 at 3:14






  • 1




    $begingroup$
    Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
    $endgroup$
    – Dr Xorile
    Feb 10 at 6:22






  • 1




    $begingroup$
    I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
    $endgroup$
    – Steve Bennett
    Feb 10 at 11:01






  • 1




    $begingroup$
    @Nautilus TAG YOU'RE IT!
    $endgroup$
    – Riddler
    Feb 14 at 1:21















4












$begingroup$


I have a short and bitter-sweet riddle for the community this evening. As always, I hope you enjoy it; good luck!




I want to play a game of tag; however, there are some very important rules:



  • We both start at the same point.

    • You cannot tag until the third turn or greater.


  • Each turn you take one step.

  • Each turn I double the number of steps I take.

    • Our stride is exactly the same.


  • We travel in a straight line.

  • We both take one initial step.

  • Our game is played on an infinitely flat plane

  • All steps are forwards, never backwards.

    • Assume we are infinitely traveling in a straight line.



Can you tag me?




Please explain your answer.



Hint:




Your step is on top, mine on bottom. Please note the math tag.

$frac11, frac12, frac14, frac18, frac116, frac132...$











share|improve this question











$endgroup$







  • 1




    $begingroup$
    Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
    $endgroup$
    – Krad Cigol
    Feb 10 at 3:09










  • $begingroup$
    @KradCigol I've updated my post to clarify this question and another.
    $endgroup$
    – PerpetualJ
    Feb 10 at 3:14






  • 1




    $begingroup$
    Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
    $endgroup$
    – Dr Xorile
    Feb 10 at 6:22






  • 1




    $begingroup$
    I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
    $endgroup$
    – Steve Bennett
    Feb 10 at 11:01






  • 1




    $begingroup$
    @Nautilus TAG YOU'RE IT!
    $endgroup$
    – Riddler
    Feb 14 at 1:21













4












4








4





$begingroup$


I have a short and bitter-sweet riddle for the community this evening. As always, I hope you enjoy it; good luck!




I want to play a game of tag; however, there are some very important rules:



  • We both start at the same point.

    • You cannot tag until the third turn or greater.


  • Each turn you take one step.

  • Each turn I double the number of steps I take.

    • Our stride is exactly the same.


  • We travel in a straight line.

  • We both take one initial step.

  • Our game is played on an infinitely flat plane

  • All steps are forwards, never backwards.

    • Assume we are infinitely traveling in a straight line.



Can you tag me?




Please explain your answer.



Hint:




Your step is on top, mine on bottom. Please note the math tag.

$frac11, frac12, frac14, frac18, frac116, frac132...$











share|improve this question











$endgroup$




I have a short and bitter-sweet riddle for the community this evening. As always, I hope you enjoy it; good luck!




I want to play a game of tag; however, there are some very important rules:



  • We both start at the same point.

    • You cannot tag until the third turn or greater.


  • Each turn you take one step.

  • Each turn I double the number of steps I take.

    • Our stride is exactly the same.


  • We travel in a straight line.

  • We both take one initial step.

  • Our game is played on an infinitely flat plane

  • All steps are forwards, never backwards.

    • Assume we are infinitely traveling in a straight line.



Can you tag me?




Please explain your answer.



Hint:




Your step is on top, mine on bottom. Please note the math tag.

$frac11, frac12, frac14, frac18, frac116, frac132...$








riddle mathematics knowledge lateral-thinking






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Feb 13 at 17:02







PerpetualJ

















asked Feb 10 at 1:35









PerpetualJPerpetualJ

4,012544




4,012544







  • 1




    $begingroup$
    Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
    $endgroup$
    – Krad Cigol
    Feb 10 at 3:09










  • $begingroup$
    @KradCigol I've updated my post to clarify this question and another.
    $endgroup$
    – PerpetualJ
    Feb 10 at 3:14






  • 1




    $begingroup$
    Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
    $endgroup$
    – Dr Xorile
    Feb 10 at 6:22






  • 1




    $begingroup$
    I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
    $endgroup$
    – Steve Bennett
    Feb 10 at 11:01






  • 1




    $begingroup$
    @Nautilus TAG YOU'RE IT!
    $endgroup$
    – Riddler
    Feb 14 at 1:21












  • 1




    $begingroup$
    Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
    $endgroup$
    – Krad Cigol
    Feb 10 at 3:09










  • $begingroup$
    @KradCigol I've updated my post to clarify this question and another.
    $endgroup$
    – PerpetualJ
    Feb 10 at 3:14






  • 1




    $begingroup$
    Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
    $endgroup$
    – Dr Xorile
    Feb 10 at 6:22






  • 1




    $begingroup$
    I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
    $endgroup$
    – Steve Bennett
    Feb 10 at 11:01






  • 1




    $begingroup$
    @Nautilus TAG YOU'RE IT!
    $endgroup$
    – Riddler
    Feb 14 at 1:21







1




1




$begingroup$
Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
$endgroup$
– Krad Cigol
Feb 10 at 3:09




$begingroup$
Can paths be different? Will you try your best not to get caught, or will you take a path where you can get caught?
$endgroup$
– Krad Cigol
Feb 10 at 3:09












$begingroup$
@KradCigol I've updated my post to clarify this question and another.
$endgroup$
– PerpetualJ
Feb 10 at 3:14




$begingroup$
@KradCigol I've updated my post to clarify this question and another.
$endgroup$
– PerpetualJ
Feb 10 at 3:14




1




1




$begingroup$
Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
$endgroup$
– Dr Xorile
Feb 10 at 6:22




$begingroup$
Are all steps the same length? Are the turns sequential? Each turn is a straight line, but can you reorient between turns?
$endgroup$
– Dr Xorile
Feb 10 at 6:22




1




1




$begingroup$
I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
$endgroup$
– Steve Bennett
Feb 10 at 11:01




$begingroup$
I'm confused by both parties starting at the same point. If we're next to each other, hasn't the tagger already won?
$endgroup$
– Steve Bennett
Feb 10 at 11:01




1




1




$begingroup$
@Nautilus TAG YOU'RE IT!
$endgroup$
– Riddler
Feb 14 at 1:21




$begingroup$
@Nautilus TAG YOU'RE IT!
$endgroup$
– Riddler
Feb 14 at 1:21










8 Answers
8






active

oldest

votes


















3












$begingroup$

So, if we both go




infinitely many times




then your position will be




$x = 1 + 2 + 4 + 8 + 16 + dots$
$x = 1 + 2(1 + 2 + 4 + 8 + dots)$
$x = 1+2x$
$x = -frac12$




and my position will be




$1+1+1+1+1+dots= -frac12$, shown by Dirichlet regularization




hence




I tag you.







share|improve this answer









$endgroup$








  • 5




    $begingroup$
    -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
    $endgroup$
    – Kevin
    Feb 13 at 16:32


















7












$begingroup$

The answer is




Yes.




We can do this because:




Geometry. If we were on a plane, you would escape, but if we were on a non-Euclidean surface (like a torus or a sphere) you would come up to me from behind and I could tag you. Since earth is a sphere, this seems to be a safe assumption. This also justifies the knowledge tag.







share|improve this answer











$endgroup$












  • $begingroup$
    Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
    $endgroup$
    – PerpetualJ
    Feb 10 at 3:37











  • $begingroup$
    @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
    $endgroup$
    – Krad Cigol
    Feb 10 at 4:07


















5












$begingroup$

The answer is:




Yes. Either A tags B before the game starts,




or




A's steps are twice as long as B's, and so tag occurs at the end of round 1.







share|improve this answer









$endgroup$












  • $begingroup$
    Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
    $endgroup$
    – PerpetualJ
    Feb 10 at 1:41


















4












$begingroup$

The answer is




Yes




Why?




I have really long arms







share|improve this answer









$endgroup$




















    3












    $begingroup$

    It's not as sensational as the other answers, but there's a genuine, mathematically sound argument to be made that the answer is simply




    No.




    The distance $d_you$ you've traveled after $n$ turns is $d_you = n^2$, and the distance $d_me$ I've traveled is $d_me = n$.




    Using big-O notation, $O(n^2)$ grows faster than $O(n)$, meaning I will never catch you.




    One important thing to note that the accepted answer fails to account for:




    While $sum_n=1^infty n^2$ and $sum_n=1^infty n$ are both equal to $-frac12$ based on certain mathematical arguments, the naive approaches that argue that they both grow without bound are still valid in other contexts - and I would argue those contexts are the ones that apply to our puzzle here. See the Wikipedia articles (https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF and https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF), which say: "Therefore, any totally regular summation method [for $sum_n=1^infty n^2$] gives a sum of infinity," and, "In the context of the extended real number line, $sum_n=1^infty n = infty$, since its sequence of partial sums increases monotonically without bound."




    The reason this is the more appropriate way to approach the puzzle is




    At any given moment in our game, we'll have only played for a finite amount of time. The game will continue without end forever, but the amount of time we'll have played at any moment is arbitrarily large, which is not the same thing as infinite. This puzzle and this Math.SE question I asked a few years ago explore the distinction and show some of its consequences.







    share|improve this answer











    $endgroup$












    • $begingroup$
      This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
      $endgroup$
      – PerpetualJ
      Feb 13 at 17:01










    • $begingroup$
      @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
      $endgroup$
      – Kevin
      Feb 14 at 18:21



















    2












    $begingroup$

    Kinda lame, but




    Yes, if you have low stamina and takes some breaks?







    share|improve this answer









    $endgroup$




















      2












      $begingroup$

      You say it's an infinite plane so:




      Let's take a well known graph that stretches off to infinity; $y = frac1x$
      enter image description here

      As the values in x reach positive infinity, they become closer and closer to y = 0, until eventually it flips over to negative y, and the x becomes negative infinity, where the x values then increase to near y = 0.


      One could liken this graph to your problem, I believe that as the number of steps taken doubles every time, it would go from a positively infinite number back to negatively infinite, and eventually catch back up again with the other player who only moves 1 step at a time.







      share|improve this answer









      $endgroup$




















        2












        $begingroup$

        The answer is




        yes




        Explanation:




        you did not mention what type of geometric plane so it might be curved plane where one meet again







        share|improve this answer











        $endgroup$












          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "559"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f79495%2flets-play-tag%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          8 Answers
          8






          active

          oldest

          votes








          8 Answers
          8






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          3












          $begingroup$

          So, if we both go




          infinitely many times




          then your position will be




          $x = 1 + 2 + 4 + 8 + 16 + dots$
          $x = 1 + 2(1 + 2 + 4 + 8 + dots)$
          $x = 1+2x$
          $x = -frac12$




          and my position will be




          $1+1+1+1+1+dots= -frac12$, shown by Dirichlet regularization




          hence




          I tag you.







          share|improve this answer









          $endgroup$








          • 5




            $begingroup$
            -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
            $endgroup$
            – Kevin
            Feb 13 at 16:32















          3












          $begingroup$

          So, if we both go




          infinitely many times




          then your position will be




          $x = 1 + 2 + 4 + 8 + 16 + dots$
          $x = 1 + 2(1 + 2 + 4 + 8 + dots)$
          $x = 1+2x$
          $x = -frac12$




          and my position will be




          $1+1+1+1+1+dots= -frac12$, shown by Dirichlet regularization




          hence




          I tag you.







          share|improve this answer









          $endgroup$








          • 5




            $begingroup$
            -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
            $endgroup$
            – Kevin
            Feb 13 at 16:32













          3












          3








          3





          $begingroup$

          So, if we both go




          infinitely many times




          then your position will be




          $x = 1 + 2 + 4 + 8 + 16 + dots$
          $x = 1 + 2(1 + 2 + 4 + 8 + dots)$
          $x = 1+2x$
          $x = -frac12$




          and my position will be




          $1+1+1+1+1+dots= -frac12$, shown by Dirichlet regularization




          hence




          I tag you.







          share|improve this answer









          $endgroup$



          So, if we both go




          infinitely many times




          then your position will be




          $x = 1 + 2 + 4 + 8 + 16 + dots$
          $x = 1 + 2(1 + 2 + 4 + 8 + dots)$
          $x = 1+2x$
          $x = -frac12$




          and my position will be




          $1+1+1+1+1+dots= -frac12$, shown by Dirichlet regularization




          hence




          I tag you.








          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Feb 11 at 15:22









          athinathin

          8,25022676




          8,25022676







          • 5




            $begingroup$
            -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
            $endgroup$
            – Kevin
            Feb 13 at 16:32












          • 5




            $begingroup$
            -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
            $endgroup$
            – Kevin
            Feb 13 at 16:32







          5




          5




          $begingroup$
          -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
          $endgroup$
          – Kevin
          Feb 13 at 16:32




          $begingroup$
          -1 As I argue in my answer, the naive approaches that give $sum_x^infty n^2$ and $sum_x^infty n$ equal to $infty$ are still correct in some contexts, and those contexts are actually the more reasonable approaches for this puzzle.
          $endgroup$
          – Kevin
          Feb 13 at 16:32











          7












          $begingroup$

          The answer is




          Yes.




          We can do this because:




          Geometry. If we were on a plane, you would escape, but if we were on a non-Euclidean surface (like a torus or a sphere) you would come up to me from behind and I could tag you. Since earth is a sphere, this seems to be a safe assumption. This also justifies the knowledge tag.







          share|improve this answer











          $endgroup$












          • $begingroup$
            Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
            $endgroup$
            – PerpetualJ
            Feb 10 at 3:37











          • $begingroup$
            @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
            $endgroup$
            – Krad Cigol
            Feb 10 at 4:07















          7












          $begingroup$

          The answer is




          Yes.




          We can do this because:




          Geometry. If we were on a plane, you would escape, but if we were on a non-Euclidean surface (like a torus or a sphere) you would come up to me from behind and I could tag you. Since earth is a sphere, this seems to be a safe assumption. This also justifies the knowledge tag.







          share|improve this answer











          $endgroup$












          • $begingroup$
            Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
            $endgroup$
            – PerpetualJ
            Feb 10 at 3:37











          • $begingroup$
            @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
            $endgroup$
            – Krad Cigol
            Feb 10 at 4:07













          7












          7








          7





          $begingroup$

          The answer is




          Yes.




          We can do this because:




          Geometry. If we were on a plane, you would escape, but if we were on a non-Euclidean surface (like a torus or a sphere) you would come up to me from behind and I could tag you. Since earth is a sphere, this seems to be a safe assumption. This also justifies the knowledge tag.







          share|improve this answer











          $endgroup$



          The answer is




          Yes.




          We can do this because:




          Geometry. If we were on a plane, you would escape, but if we were on a non-Euclidean surface (like a torus or a sphere) you would come up to me from behind and I could tag you. Since earth is a sphere, this seems to be a safe assumption. This also justifies the knowledge tag.








          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Feb 10 at 3:17

























          answered Feb 10 at 3:10









          Krad CigolKrad Cigol

          896210




          896210











          • $begingroup$
            Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
            $endgroup$
            – PerpetualJ
            Feb 10 at 3:37











          • $begingroup$
            @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
            $endgroup$
            – Krad Cigol
            Feb 10 at 4:07
















          • $begingroup$
            Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
            $endgroup$
            – PerpetualJ
            Feb 10 at 3:37











          • $begingroup$
            @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
            $endgroup$
            – Krad Cigol
            Feb 10 at 4:07















          $begingroup$
          Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
          $endgroup$
          – PerpetualJ
          Feb 10 at 3:37





          $begingroup$
          Ahhh, nice adjustment; you're close with your thinking, serves me right for not thinking about lateral solutions. The real question is, would I escape, even if the plane is infinite? This is definitely a suitable answer to the way the question was originally phrased so don't remove the edit, just edit with a new guess. I'll be awarding $+50$ bounty for thinking outside the box with your spheroid solution.
          $endgroup$
          – PerpetualJ
          Feb 10 at 3:37













          $begingroup$
          @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
          $endgroup$
          – Krad Cigol
          Feb 10 at 4:07




          $begingroup$
          @PerpetualJ: Thanks! In the infinite plane - straight line case, it does seem like you’ll escape. I’ll see if I can figure it out.
          $endgroup$
          – Krad Cigol
          Feb 10 at 4:07











          5












          $begingroup$

          The answer is:




          Yes. Either A tags B before the game starts,




          or




          A's steps are twice as long as B's, and so tag occurs at the end of round 1.







          share|improve this answer









          $endgroup$












          • $begingroup$
            Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
            $endgroup$
            – PerpetualJ
            Feb 10 at 1:41















          5












          $begingroup$

          The answer is:




          Yes. Either A tags B before the game starts,




          or




          A's steps are twice as long as B's, and so tag occurs at the end of round 1.







          share|improve this answer









          $endgroup$












          • $begingroup$
            Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
            $endgroup$
            – PerpetualJ
            Feb 10 at 1:41













          5












          5








          5





          $begingroup$

          The answer is:




          Yes. Either A tags B before the game starts,




          or




          A's steps are twice as long as B's, and so tag occurs at the end of round 1.







          share|improve this answer









          $endgroup$



          The answer is:




          Yes. Either A tags B before the game starts,




          or




          A's steps are twice as long as B's, and so tag occurs at the end of round 1.








          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Feb 10 at 1:40









          JonMark PerryJonMark Perry

          19.8k64094




          19.8k64094











          • $begingroup$
            Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
            $endgroup$
            – PerpetualJ
            Feb 10 at 1:41
















          • $begingroup$
            Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
            $endgroup$
            – PerpetualJ
            Feb 10 at 1:41















          $begingroup$
          Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
          $endgroup$
          – PerpetualJ
          Feb 10 at 1:41




          $begingroup$
          Very good attempt, but note the knowledge tag. :) +1 for taking the same route my daughter tries every time! HAHA
          $endgroup$
          – PerpetualJ
          Feb 10 at 1:41











          4












          $begingroup$

          The answer is




          Yes




          Why?




          I have really long arms







          share|improve this answer









          $endgroup$

















            4












            $begingroup$

            The answer is




            Yes




            Why?




            I have really long arms







            share|improve this answer









            $endgroup$















              4












              4








              4





              $begingroup$

              The answer is




              Yes




              Why?




              I have really long arms







              share|improve this answer









              $endgroup$



              The answer is




              Yes




              Why?




              I have really long arms








              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Feb 11 at 13:53









              CubemasterCubemaster

              1,577333




              1,577333





















                  3












                  $begingroup$

                  It's not as sensational as the other answers, but there's a genuine, mathematically sound argument to be made that the answer is simply




                  No.




                  The distance $d_you$ you've traveled after $n$ turns is $d_you = n^2$, and the distance $d_me$ I've traveled is $d_me = n$.




                  Using big-O notation, $O(n^2)$ grows faster than $O(n)$, meaning I will never catch you.




                  One important thing to note that the accepted answer fails to account for:




                  While $sum_n=1^infty n^2$ and $sum_n=1^infty n$ are both equal to $-frac12$ based on certain mathematical arguments, the naive approaches that argue that they both grow without bound are still valid in other contexts - and I would argue those contexts are the ones that apply to our puzzle here. See the Wikipedia articles (https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF and https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF), which say: "Therefore, any totally regular summation method [for $sum_n=1^infty n^2$] gives a sum of infinity," and, "In the context of the extended real number line, $sum_n=1^infty n = infty$, since its sequence of partial sums increases monotonically without bound."




                  The reason this is the more appropriate way to approach the puzzle is




                  At any given moment in our game, we'll have only played for a finite amount of time. The game will continue without end forever, but the amount of time we'll have played at any moment is arbitrarily large, which is not the same thing as infinite. This puzzle and this Math.SE question I asked a few years ago explore the distinction and show some of its consequences.







                  share|improve this answer











                  $endgroup$












                  • $begingroup$
                    This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                    $endgroup$
                    – PerpetualJ
                    Feb 13 at 17:01










                  • $begingroup$
                    @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                    $endgroup$
                    – Kevin
                    Feb 14 at 18:21
















                  3












                  $begingroup$

                  It's not as sensational as the other answers, but there's a genuine, mathematically sound argument to be made that the answer is simply




                  No.




                  The distance $d_you$ you've traveled after $n$ turns is $d_you = n^2$, and the distance $d_me$ I've traveled is $d_me = n$.




                  Using big-O notation, $O(n^2)$ grows faster than $O(n)$, meaning I will never catch you.




                  One important thing to note that the accepted answer fails to account for:




                  While $sum_n=1^infty n^2$ and $sum_n=1^infty n$ are both equal to $-frac12$ based on certain mathematical arguments, the naive approaches that argue that they both grow without bound are still valid in other contexts - and I would argue those contexts are the ones that apply to our puzzle here. See the Wikipedia articles (https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF and https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF), which say: "Therefore, any totally regular summation method [for $sum_n=1^infty n^2$] gives a sum of infinity," and, "In the context of the extended real number line, $sum_n=1^infty n = infty$, since its sequence of partial sums increases monotonically without bound."




                  The reason this is the more appropriate way to approach the puzzle is




                  At any given moment in our game, we'll have only played for a finite amount of time. The game will continue without end forever, but the amount of time we'll have played at any moment is arbitrarily large, which is not the same thing as infinite. This puzzle and this Math.SE question I asked a few years ago explore the distinction and show some of its consequences.







                  share|improve this answer











                  $endgroup$












                  • $begingroup$
                    This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                    $endgroup$
                    – PerpetualJ
                    Feb 13 at 17:01










                  • $begingroup$
                    @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                    $endgroup$
                    – Kevin
                    Feb 14 at 18:21














                  3












                  3








                  3





                  $begingroup$

                  It's not as sensational as the other answers, but there's a genuine, mathematically sound argument to be made that the answer is simply




                  No.




                  The distance $d_you$ you've traveled after $n$ turns is $d_you = n^2$, and the distance $d_me$ I've traveled is $d_me = n$.




                  Using big-O notation, $O(n^2)$ grows faster than $O(n)$, meaning I will never catch you.




                  One important thing to note that the accepted answer fails to account for:




                  While $sum_n=1^infty n^2$ and $sum_n=1^infty n$ are both equal to $-frac12$ based on certain mathematical arguments, the naive approaches that argue that they both grow without bound are still valid in other contexts - and I would argue those contexts are the ones that apply to our puzzle here. See the Wikipedia articles (https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF and https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF), which say: "Therefore, any totally regular summation method [for $sum_n=1^infty n^2$] gives a sum of infinity," and, "In the context of the extended real number line, $sum_n=1^infty n = infty$, since its sequence of partial sums increases monotonically without bound."




                  The reason this is the more appropriate way to approach the puzzle is




                  At any given moment in our game, we'll have only played for a finite amount of time. The game will continue without end forever, but the amount of time we'll have played at any moment is arbitrarily large, which is not the same thing as infinite. This puzzle and this Math.SE question I asked a few years ago explore the distinction and show some of its consequences.







                  share|improve this answer











                  $endgroup$



                  It's not as sensational as the other answers, but there's a genuine, mathematically sound argument to be made that the answer is simply




                  No.




                  The distance $d_you$ you've traveled after $n$ turns is $d_you = n^2$, and the distance $d_me$ I've traveled is $d_me = n$.




                  Using big-O notation, $O(n^2)$ grows faster than $O(n)$, meaning I will never catch you.




                  One important thing to note that the accepted answer fails to account for:




                  While $sum_n=1^infty n^2$ and $sum_n=1^infty n$ are both equal to $-frac12$ based on certain mathematical arguments, the naive approaches that argue that they both grow without bound are still valid in other contexts - and I would argue those contexts are the ones that apply to our puzzle here. See the Wikipedia articles (https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_%E2%8B%AF and https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E2%8B%AF), which say: "Therefore, any totally regular summation method [for $sum_n=1^infty n^2$] gives a sum of infinity," and, "In the context of the extended real number line, $sum_n=1^infty n = infty$, since its sequence of partial sums increases monotonically without bound."




                  The reason this is the more appropriate way to approach the puzzle is




                  At any given moment in our game, we'll have only played for a finite amount of time. The game will continue without end forever, but the amount of time we'll have played at any moment is arbitrarily large, which is not the same thing as infinite. This puzzle and this Math.SE question I asked a few years ago explore the distinction and show some of its consequences.








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited Feb 14 at 21:27

























                  answered Feb 13 at 16:29









                  KevinKevin

                  1,0171821




                  1,0171821











                  • $begingroup$
                    This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                    $endgroup$
                    – PerpetualJ
                    Feb 13 at 17:01










                  • $begingroup$
                    @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                    $endgroup$
                    – Kevin
                    Feb 14 at 18:21

















                  • $begingroup$
                    This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                    $endgroup$
                    – PerpetualJ
                    Feb 13 at 17:01










                  • $begingroup$
                    @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                    $endgroup$
                    – Kevin
                    Feb 14 at 18:21
















                  $begingroup$
                  This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                  $endgroup$
                  – PerpetualJ
                  Feb 13 at 17:01




                  $begingroup$
                  This is a very thorough answer! My puzzle was technically focused on convergence of the reciprocals of powers of two where starting from 1, as $n$ steps approaches infinity, we converge on 2. $1, 1.5, 1.75, 1.875, 1.9375...$
                  $endgroup$
                  – PerpetualJ
                  Feb 13 at 17:01












                  $begingroup$
                  @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                  $endgroup$
                  – Kevin
                  Feb 14 at 18:21





                  $begingroup$
                  @PerpetualJ I don't think that convergence has any useful meaning in your puzzle. The fraction $frac1n^2$ is the fraction of the distance you travel that I travel on turn $n$. It makes no meaningful sense to sum up those fractions. What would the sum represent?
                  $endgroup$
                  – Kevin
                  Feb 14 at 18:21












                  2












                  $begingroup$

                  Kinda lame, but




                  Yes, if you have low stamina and takes some breaks?







                  share|improve this answer









                  $endgroup$

















                    2












                    $begingroup$

                    Kinda lame, but




                    Yes, if you have low stamina and takes some breaks?







                    share|improve this answer









                    $endgroup$















                      2












                      2








                      2





                      $begingroup$

                      Kinda lame, but




                      Yes, if you have low stamina and takes some breaks?







                      share|improve this answer









                      $endgroup$



                      Kinda lame, but




                      Yes, if you have low stamina and takes some breaks?








                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered Feb 11 at 12:21









                      Henrique ValleHenrique Valle

                      2113




                      2113





















                          2












                          $begingroup$

                          You say it's an infinite plane so:




                          Let's take a well known graph that stretches off to infinity; $y = frac1x$
                          enter image description here

                          As the values in x reach positive infinity, they become closer and closer to y = 0, until eventually it flips over to negative y, and the x becomes negative infinity, where the x values then increase to near y = 0.


                          One could liken this graph to your problem, I believe that as the number of steps taken doubles every time, it would go from a positively infinite number back to negatively infinite, and eventually catch back up again with the other player who only moves 1 step at a time.







                          share|improve this answer









                          $endgroup$

















                            2












                            $begingroup$

                            You say it's an infinite plane so:




                            Let's take a well known graph that stretches off to infinity; $y = frac1x$
                            enter image description here

                            As the values in x reach positive infinity, they become closer and closer to y = 0, until eventually it flips over to negative y, and the x becomes negative infinity, where the x values then increase to near y = 0.


                            One could liken this graph to your problem, I believe that as the number of steps taken doubles every time, it would go from a positively infinite number back to negatively infinite, and eventually catch back up again with the other player who only moves 1 step at a time.







                            share|improve this answer









                            $endgroup$















                              2












                              2








                              2





                              $begingroup$

                              You say it's an infinite plane so:




                              Let's take a well known graph that stretches off to infinity; $y = frac1x$
                              enter image description here

                              As the values in x reach positive infinity, they become closer and closer to y = 0, until eventually it flips over to negative y, and the x becomes negative infinity, where the x values then increase to near y = 0.


                              One could liken this graph to your problem, I believe that as the number of steps taken doubles every time, it would go from a positively infinite number back to negatively infinite, and eventually catch back up again with the other player who only moves 1 step at a time.







                              share|improve this answer









                              $endgroup$



                              You say it's an infinite plane so:




                              Let's take a well known graph that stretches off to infinity; $y = frac1x$
                              enter image description here

                              As the values in x reach positive infinity, they become closer and closer to y = 0, until eventually it flips over to negative y, and the x becomes negative infinity, where the x values then increase to near y = 0.


                              One could liken this graph to your problem, I believe that as the number of steps taken doubles every time, it would go from a positively infinite number back to negatively infinite, and eventually catch back up again with the other player who only moves 1 step at a time.








                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered Feb 11 at 12:48









                              AHKieranAHKieran

                              5,2911042




                              5,2911042





















                                  2












                                  $begingroup$

                                  The answer is




                                  yes




                                  Explanation:




                                  you did not mention what type of geometric plane so it might be curved plane where one meet again







                                  share|improve this answer











                                  $endgroup$

















                                    2












                                    $begingroup$

                                    The answer is




                                    yes




                                    Explanation:




                                    you did not mention what type of geometric plane so it might be curved plane where one meet again







                                    share|improve this answer











                                    $endgroup$















                                      2












                                      2








                                      2





                                      $begingroup$

                                      The answer is




                                      yes




                                      Explanation:




                                      you did not mention what type of geometric plane so it might be curved plane where one meet again







                                      share|improve this answer











                                      $endgroup$



                                      The answer is




                                      yes




                                      Explanation:




                                      you did not mention what type of geometric plane so it might be curved plane where one meet again








                                      share|improve this answer














                                      share|improve this answer



                                      share|improve this answer








                                      edited Feb 22 at 6:21









                                      athin

                                      8,25022676




                                      8,25022676










                                      answered Feb 10 at 13:19







                                      user56760


































                                          draft saved

                                          draft discarded
















































                                          Thanks for contributing an answer to Puzzling Stack Exchange!


                                          • Please be sure to answer the question. Provide details and share your research!

                                          But avoid


                                          • Asking for help, clarification, or responding to other answers.

                                          • Making statements based on opinion; back them up with references or personal experience.

                                          Use MathJax to format equations. MathJax reference.


                                          To learn more, see our tips on writing great answers.




                                          draft saved


                                          draft discarded














                                          StackExchange.ready(
                                          function ()
                                          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f79495%2flets-play-tag%23new-answer', 'question_page');

                                          );

                                          Post as a guest















                                          Required, but never shown





















































                                          Required, but never shown














                                          Required, but never shown












                                          Required, but never shown







                                          Required, but never shown

































                                          Required, but never shown














                                          Required, but never shown












                                          Required, but never shown







                                          Required, but never shown






                                          Popular posts from this blog

                                          How to check contact read email or not when send email to Individual?

                                          Displaying single band from multi-band raster using QGIS

                                          How many registers does an x86_64 CPU actually have?