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I am trying to measure 100m for a children's foot race, but I forgot to bring my measuring wheel. I know that each of my steps is between 0.9m and 1.1m (sampled at uniform). I can only take full steps - no half steps. I also have an unlimited supply of cones that I can place on the ground. How can I measure 100m or as close as possible to it?

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Measure 100 full steps and mark the end point with a cone. Do this a large odd number of times, let's say 1001 (or 2n+1). Then, starting with the cone nearest to your starting point, count 501 (or n+1) cones in order. The 501st nearest cone is your 100-metre marker. The larger your number of attempts, the closer this cone should be to exactly 100m.

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    $\begingroup$ Correct! That's the approach I had in mind. $\endgroup$ May 19, 2023 at 3:02
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    $\begingroup$ @DmitryKamenetsky That said, for a children's foot race I'd probably just measure it once and call that 100m :P $\endgroup$
    – Jafe
    May 19, 2023 at 5:21
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    $\begingroup$ So, the answer is median of many samples? $\endgroup$
    – justhalf
    May 19, 2023 at 7:57
  • $\begingroup$ @Jafe yeah that probably works too :) $\endgroup$ May 19, 2023 at 8:01
  • $\begingroup$ @justhalf yep pretty much. I was thinking that there could be another pass between the smallest and largest samples to converge faster to the 100, but not sure that it would be faster. $\endgroup$ May 19, 2023 at 8:02

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