A 24-year-old male presents with a painless, palpable bony mass on the left knee. What is the most likely diagnosis?

The diagnosis of an osteochondroma is supported by the presentation of a painless, palpable bony mass, which is a classic characteristic of this condition. Osteochondromas typically manifest as benign bone tumors that arise from the growth plate, and they often present in adolescents and young adults. They are often observed as incidental findings, but palpable masses are common when they occur near joints, like the knee in this case.

In contrast, while osteosarcoma and Ewing sarcoma can present with bone masses, they are usually associated with pain and more aggressive features. Osteosarcoma tends to be found in the metaphysis of long bones and often has a painful presentation, while Ewing sarcoma is more inflammatory and often presents with systemic symptoms alongside localized pain. Chondrosarcoma, although it can also present as a bony mass, is more typically found in older adults and usually has a painful profile. Therefore, the benign nature and typical presentation of an osteochondroma, especially in a young male with a palpable, painless mass, aligns appropriately with the most likely diagnosis.