One solution starts out with the farmer bringing the chicken across and then return empty handed. The farmer then brings the bag of grain to the far side, but bringing the chicken back on the return trip. The farmer then brings the fox to the far side and return empty handed. Finally, the farmer brings the chicken across the river again, thus fulfilling the goal.
There is one other solution: once again the farmer starts by bringing the chicken across and then return empty handed. The farmer then brings the fox to the far side, but bringing the chicken back on the return trip. The farmer then brings the bag of grain to the far side and return empty handed. Finally, the farmer brings the chicken across the river again, thus fulfilling the goal.