May 2015 - Archimedean Cattle

This is based on a problem set by Archimedes. There is a field with many cattle. There are white bulls and cows, black bulls and cows, and yellow bulls and cows. Here are some clues:

Three times the number of white bulls makes the number of black bulls and yellow bulls.
Twice the number of white cows makes the number of yellow cattle.
Twice the number of black bulls makes the number of white bulls and yellow bulls.
Three times the number of black cows makes the number of white cattle and yellow cows.
Twice the number of yellow bulls makes the number of white cows and black cattle.
The number of white bulls and black cows make one less than a square number.

What is the smallest possible non-zero number of white cows?

The deadline has passed. You can see the answer or go to the Hall of Fame.

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