A farmer was showing a mathematician around his fields. Frustrated by his endless demonstrations of cerebral aptitude, the farmer decided to teach him a lesson. He took the mathematician to a field that packed with hundreds of grazing sheep, all of them milling about and moving around.
“If you can guess the exact number of sheep in this field,” challenged the farmer, “I’ll give you all of them!”
The mathematician looked thoughtful for a moment, and his eyes darted back and forth rapidly. Presently he announced, “Two hundred and fourteen.”
The farmer gaped, too stunned to calculate his loss yet, “How on Earth did you do that? There’s no way you could have counted all those sheep that fast!”
“You’re absolutely right,” the mathematician agreed. “I counted all the legs, and then divided by four.”