perplexus.info :: Numbers : What a waist

What a waist (Posted on 2003-05-28)

A woman's "measurements" are three numbers that measure, in order, the inches around her bust, waist and hips.
Now, a certain beauty contest winner had a 36-23-34 figure.
Although no two contestants had exactly the same measurements, the two runners-up differed by less than an inch in each measurement from the winner and the waist of each was two-thirds the hips of the other.

If the sum of the three measurements was the same for all three girls, what were the vital statistics of the two runners-up (the tape is accurate to only a quarter of an inch)?

Submitted by DJ

Rating: 4.4444 (9 votes)

Solution: (Hide)

36¼-23-33¾ and 36-22½-34½

Since the tape is only accurate to ¼" for all measurements (meaning each measurement is an integer multiple of ¼"), and each the two runners-up waist is two-thirds of the other's hips, then both hip measurements must be multiples of ¾".
These numbers are between 33" and 35" (non-inclusive), and the only values that fit these parameters are 33¾", two-thirds of which is 22½", and 34½", two-thirds of which is 23".
So, one of the girls in question has a 23" waist and a 33¾" hip measurement; the other has a 22½" waist and 34½" hips.

We also know that the sum of all three measurements is the same for each girl. For the winner, this is 36+23+34=93". So, the remaining (bust) measurement for the first girl above is
93-23-33¾=36¼",
and for the second,
93-22½-34½=36".

Therefore, the two runners-up must have measurements :
36¼-23-33¾ and 36-22½-34½

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2007-10-26 05:19:19
re: Solution	DJ	2003-05-29 16:01:19
Solution	Bryan	2003-05-28 09:51:38
Solution	Clinton Heath	2003-05-28 09:26:47

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