The Altair One Beauty Contest

 

ON THE faraway planet of Altair One, the annual beauty contest offends no-one because their world is a civilisation of hermaphrodites. Many Altairlings vie for the title of Misster World every year, and in this specific year, the competition was particularly strong.

Altairlings have a similar shape to Earthlings but are much smaller in size. Their unit of measurement is the "tad" and their tape measures are accurate only to a quarter of a tad.

The beauty contest winner, a shy young thing with pulsating scales and oozing eye-sockets had a 36 - 23 - 34 figure. Although no two contestants had exactly the same three measurements, the two runners-up differed by less than a tad in each measurement from the winner. And each of the runners'-up waist measurements were two-thirds the hip of the other.

If the sum of the three measurements were exactly the same for all three place-getters, what were the vital statistics of the two runners-up?

 

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