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New Scientist Enigma 886 – Set Square

by Brian Gladman on July 27, 2021

by Susan Denham

From Issue #2041, 3rd August 1996 (link)

Last week I watched a thrilling five-set tennis match between the two top players, Pampas and Grassy. Pampas won the first set easily and the second in a tie-break. He then lost the next two sets and towards the end of the final set the scoreboard showing the games won looked like this:

\[\begin{array}{|l|c|c|c|c|c|}\hline \mathbf{Pampas} & \mathbf{6} & \mathbf{7} & \mathbf{5} & \mathbf{0}& \mathbf{7} \\
\hline \mathbf{Grassy} & \mathbf{7} & \mathbf{2} & \mathbf{3} & \mathbf{6}& \mathbf{1} \\
\hline \end{array}\]

Pampas then went on to win the next two games (and hence the match).

I remember on a previous occasion when they met the match also went to five sets. Towards the end of the match I looked at the scoreboard and each of the two rows of games won formed a five-figure perfect square. On that occasion Grassy then went on to win in two more games.

What did the score-board look like at the very end of that match?

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5 Comments Leave one →
  1. Brian Gladman permalink

    • Frits permalink

      @Brian, Could you explain the value 315?

      I see you have gone for a general solution (without combining requirements to reduce some possibilities like fifth set scores (7,9) and (8, 10)).

      • Brian Gladman permalink

        Hi Frits,

        It was meant to be 317 but it is still way higher than it needs to be 🙂 I
        will update it to put a better limit in (279).

        Yes, I don’t do much, if any, analysis at a detailed level unless this is
        necessary to achieve a reasonable speed. I prefer simplicity over the
        extra coding (or explanation) involved in adding such constraints.

  2. I don’t think 7-6 is a valid winning score in the final set, so it shouldn’t be in pss5.

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