A child with all permanent incisors erupted but only three permanent first molars shows a large gingival bulge. What is the most likely diagnosis?

In this scenario, where a child has all permanent incisors erupted but only three permanent first molars, along with a large gingival bulge, the most likely diagnosis is idiopathic failure of eruption. This condition refers to the situation where a tooth, despite being present in the jawbone, fails to emerge into the oral cavity due to various potential reasons, without any identifiable cause.

The presence of a gingival bulge can often indicate that there is an impacted tooth beneath the gum line, which aligns with the characteristic presentation of idiopathic failure of eruption. In such cases, the treatment typically involves soft tissue exposure of the impacted tooth, allowing it to properly erupt into its functional position.

Considering the other options, while a dentigerous cyst could lead to a gingival swelling, it generally involves a tooth that is not vital and presents with other signs, making it less likely here. Abscess formation might present with pain and systemic symptoms and usually requires drainage and antibiotics, which is not mentioned. Dental trauma often leads to mobility or loss of the tooth rather than just a gingival bulge and would typically show signs of injury.

Thus, understanding the presentation of these conditions leads to the conclusion that idiopathic failure of eruption is the most fitting