# Sunday Times Teaser 3094 – There’s Always Next Year

*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?

Simple program but excrutiangly long running time

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