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Subj:.....Trading in the Philippines (S587)
          From the book 
           "More Mathematical Puzzles of Sam Loyd" 
            Edited by Martin Gardner 
            From: Dover Publications in 1960

What are the weights of the four rings?

I recently came upon an old travel book that described some of
the primitive methods once used for conducting business in the
Philippines.  The traveling merchant shown in the picture uses
a balance scale and four metal rings that serve as weights.
The rings are different weights and sizes and he carries them
on his arms like bracelets.

With these four rings, the trader can weigh anything from a
quarter of a pound up to ten pounds.  These weights enable the
trader to get within a quarter of a pound of any weight within
the limits mentioned.

What are the weights of the four rings?
 
 
 
 
 
 

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                   THE SOLUTION 
               

The four rings weigh a quarter of a pound, three quarters of a
pound, two and one quarter pounds, and six and three quarters
pounds.  By clever juggling with the weights, placing them if
need be on both sides of the scale, any weight from one quarter
to ten pounds can be weighed to the nearest quarter-pound.

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