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Archimedes' Cattle (Posted on 2004-02-17) Difficulty: 4 of 5
The sun god had a herd of cattle consisting of bulls and cows, one part of which was white, a second black, a third spotted, and a fourth brown.

Among the bulls, the number of white ones was one half plus one third the number of the black greater than the brown; the number of the black, one quarter plus one fifth the number of the spotted greater than the brown; the number of the spotted, one sixth and one seventh the number of the white greater than the brown.

Among the cows, the number of white ones was one third plus one quarter of the total black cattle; the number of the black, one quarter plus one fifth the total of the spotted cattle; the number of spotted, one fifth plus one sixth the total of the brown cattle; the number of the brown, one sixth plus one seventh the total of the white cattle.

What was the composition of the herd?

See The Solution Submitted by DJ    
Rating: 3.5000 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: full solution - exact fractions | Comment 4 of 6 |
(In reply to full solution by SilverKnight)

The exact values (with common denoninator) for SilverKnight's a,b,c,d,e,f,g,and h are:

a = 10366482/50389082
b = 7460514/50389082
c = 7358060/50389082
d = 4149387/50389082
e = 7206360/50389082
f = 4893246/50389082
g = 3515820/50389082
h = 5439213/50389082
  Posted by Brian Smith on 2004-02-18 11:32:13

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