Problem of the Week: Sheep
A sheep farmer has built an enclosure with four separate pens, as shown below. In the center of the enclosure is a rather unusual four-sided gate. Whenever three sheep enter the gate from three different sides, the fourth side of the gate opens and all three sheep enter the fourth pen.
If there are initially 24, 28, 32, and 36 sheep in the four pens, respectively, is it possible that after some time has passed there will be an equal number of sheep in each pen? What if there are initially 12, 14, 16, and 18 sheep in the four pens, respectively? In each case justify your answer by demonstrating how it can be done or by proving that it is impossible.
Winner
The winning solution to this problem was by Sourabh Chakraborty.
Other correct submissions were from Rob Brase, Christopher Haccius, and Huong Nguyen.
