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In every round of a tennis championship, assuming the highest seed in every match wins that match, in every round the highest seed plays the lowest remaining seed until the first seed and the second seed meet in the final.

If there are $N$ players, $k$ rounds, the first round we number $m=1$ and the final is round $m=k$, what is the formula for the $n^{th}$ player on court in the first round?

Where choice exists in the order in which competitors can be listed, let's assume the highest seed (lowest number) is always listed first, and the draw is arranged so the highest and next highest seeds are farthest apart. So if $k=3$, the $n^{th}$ player on court is equal to the $n^{th}$ element of $\{1,4,3,2\}$

What is the formula in terms of $n$ and $k$ for the $n^{th}$ player on court?

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    Could you explain how do you get set $\{\,1, 4, 3, 2\,\}$? Or is it a sequence? (Then $(1, 4, 3, 2)$ would be better notation.) – 2017-02-23
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    Yes, you're right, it's a sequence. – 2017-02-23
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    Anyway, could you explain how do you get it? – 2017-02-23
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    Highest seed 1 plays lowest seed 4 first. 3rd seed must then play 2nd seed in order for all 4 to play in that round. 2nd seed is placed farthest from 1st seed, being closest in value, so is listed after seed 3. – 2017-02-23

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