Editor's Note: This month we are starting a puzzle series, designed to feature some of the classic mind twisters of the literature. Each issue will carry one or two problems, plus solutions for the previous month. This is not a contest, and there is no need to send in answers. We just hope you enjoy working out Dr. Lobachevski's contributions.
The "Problema Bovinum" is attributed to Archimedes; a complete formulation of it was found in an ancient Greek manuscript in 1773. Perhaps some modern day Mensans might like to wander back nostalgically into ancient Greece and match wits with Archimedes for a solution to this old problem. Hand calculators, computers, nomographs and other modern aids are of course permitted.
The Sun God had a herd of cattle consisting of bulls and cows; one part 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 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 spotted, one sixth plus 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 the spotted, one fifth plus one sixth of the total of the brown cattle; the number of the brown, one sixth plus one seventh of the total of the white cattle. What was the composition of the herd?