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# One more that need explaining

Thu 27 May, 2004 03:43 am
This problem was proposed by Archimedes about 2200 years ago.

Compute, O friend the host of oxen of the sun, giving thy mind thereto, if thou hast a share of wisdom. Compute the number that once grazed upon the plains of the Sicilian isle Trinacria (Sicily itself) and that were divided according to color into four herds, one milk-white, one black, one yellow and one dappled. The number of bulls formed the majority in each herd and the relations between them were:
1. White bulls = yellow bulls + (1/2 + 1/3) black bulls
2. Black bulls = yellow bulls + (1/4 + 1/5) dappled bulls
3. Dappled bulls = yellow bulls + (1/6 + 1/7) white bulls
4. White cows = (1/3 + 1/4) black herd
5. Black cows = (1/4 + 1/5) dappled herd
6. Dappled cows = (1/5 + 1/6) yellow herd
7. Yellow cows = (1/6 + 1/7) white herd

If thou canst give O friend the number of bulls and cows in each herd, thou art not all knowing nor unskilled in number, but not yet to be counted among the wise. Consider however the additional relations between the bulls of the sun:
8. White bulls + Black bulls = triangular number
9. Dappled bulls + yellow bulls = square number

When thou hast then computed the totals of the herd, O friend go forth as the conqueror, and rest assured that thou art proved most skilled in the science of numbers.

Whim
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Type: Discussion • Score: 1 • Views: 787 • Replies: 2
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Tryagain

1
Thu 27 May, 2004 11:13 am
Whim, do keep up to date.

Posted: Mon May 17, 2004 9:04 am
He may have been very clever, but he only asked the question. He could never have worked out the answer.

[The smallest composite herd satisfying the first 7 conditions was found to be 50,389,082 cattle. A German investigator proved that the final solution is a 206,545 digit number starting with 7766. Later using a super computer it was found that there were five additional solutions the largest containing more than a million digits.]
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whimsical

1
Thu 27 May, 2004 03:15 pm
I saw the answer but I do not understand how the puzzle works.

How should I interpret the parts between the brackets: i.e. (1/2 + 1/3) black bulls, etc. ?

does it mean: 5/6 black bulls?
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