**From New Scientist #1681, 9th September 1989** [link]

Only eight of our statistics students have handed in sick-leave certificates this year — which, if averaged over all our complement, would amount to precisely one day’s illness per student.

All absences were of different lengths, of between 1 and 365 days duration, with none having two consecutive digits the same, and none ending in a zero. An odd coincidence was that these eight absences were such that they split into four pairs, each member of a pair being the same as its companion with the digits reversed. But what is really strange is that these four pairs shared a further interesting property. The square of each absence was also the digit-reversal of the square of its companion.

How many students did we have this year?

[enigma529]

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Run:[ @repl.it ]Solution:There were 784 students.The four pairs (and their squares) are: