Final answer:
The described symptoms of buttock pain that shoots down the legs and is relieved by sitting are indicative of sciatica, caused by the inflammation or compression of the sciatic nerve.
Step-by-step explanation:
The 68-year-old patient presenting with pain in the buttocks while walking, radiating down the legs, with associated weakness and numbness that is relieved by sitting, may be experiencing a condition known as sciatica. Sciatica is typically caused by inflammation or compression of the sciatic nerve, as seen with conditions such as a herniated disc or spinal stenosis. The relief of pain upon sitting and persistence of pain while standing is characteristic of this condition, as certain positions may alleviate the pressure on the sciatic nerve. Diagnosis is usually made based on a thorough medical history and physical examination, and can be confirmed with imaging studies like MRI if needed. Treatment may include physical therapy, medications, and in severe cases, surgery.