Pityriasis rosea: This condition is characterized by a herald patch followed by a secondary eruption of flat, ovoid, scaly patches on the torso, often without itching or pain. The rash's appearance and distribution, along with the absence of symptoms like itching or pain, make pityriasis rosea a strong candidate.

Tinea corporis (ringworm): Although typically itchy, some cases of tinea corporis can present with minimal symptoms. The flat, ovoid shape could fit, especially if the rash is in its early stages or not fully developed.
Nummular dermatitis: This condition presents with coin-shaped patches of dermatitis, which could be described as ovoid. While it often itches, the absence of itching doesn't rule it out entirely, especially in mild cases.
Seborrheic dermatitis: While more commonly associated with the scalp, face, and areas rich in sebaceous glands, seborrheic dermatitis can occasionally present on the torso with a flat, ovoid appearance, particularly in the context of a more widespread eruption.

Cutaneous lymphoma (e.g., mycosis fungoides): Although rare, cutaneous lymphomas can present with a wide range of skin manifestations, including flat, ovoid patches. Given the potential severity of this diagnosis, it's crucial not to miss it, even if the presentation seems atypical.
Secondary syphilis: This condition can cause a wide variety of skin rashes, including flat, ovoid patches. The absence of itching or pain and the potential for serious complications if left untreated make it a "do not miss" diagnosis.

Sarcoidosis: This systemic disease can manifest with skin lesions, including flat, ovoid rashes. While rare, sarcoidosis is an important consideration due to its systemic implications.
Mastocytosis: Characterized by an accumulation of mast cells in the skin, mastocytosis can present with a variety of skin lesions, including flat, ovoid patches. The condition is rare and might not be the first consideration but should be kept in mind, especially if other symptoms are present.