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Sunday Times Teaser 3094 – There’s Always Next Year

by Brian Gladman on January 7, 2022

by Danny Roth

Published Sunday January 09 2022 (link)

\[\begin{array}{|c|c|c|c|c|c|}\hline Year & 2018 & 2019 & 2020 & 2021 & 2022 \\
\hline Pass\;Rate\;(\%) & 30 & 32 & 35 & 36 & X \\
\hline \end{array}\]

George and Martha annually examine around 500 candidates (give or take 5%). It is board policy to pass about a third of the entrants but the precise recent percentage pass rates were as above.

The number of entrants in each year up to 2021 was different as was the number of successful candidates. George told Martha of the number of entries for 2022 (different again) and Martha calculated that, if X were to be once again a whole number (also different again but within the above range), the total number of successful candidates over the five-year period would be a perfect square.

How many entries are there for 2022 and how many successful candidates did Martha calculate for 2022?

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4 Comments Leave one →
  1. Brian Gladman permalink

  2. GeoffR permalink

  3. John Z permalink

    Simple program but excrutiangly long running time

  4. John Z permalink

    Permuting over 4 candidate numbers instead of 5 reduces running time considerably

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