**Core Concept**
The question is testing the association between a specific clinical presentation and a particular congenital syndrome. The underlying principle involves recognizing a characteristic physical examination finding that is strongly suggestive of a genetic disorder.

**Why the Correct Answer is Right**
The child's presentation of mental retardation and a skin rash on the cheeks is highly suggestive of **Fragile X syndrome**. This is because Fragile X syndrome is the most common cause of inherited intellectual disability, and the skin rash on the cheeks, also known as **mitten-hand sign**, is a characteristic physical examination finding in this condition. The mitten-hand sign is due to the presence of a triangular or mitten-shaped hand with a short 4th finger. Fragile X syndrome is caused by an expansion of the CGG repeat in the FMR1 gene on the X chromosome, leading to the silencing of the gene and a deficiency of the FMRP protein, which is essential for normal brain development.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the child's presentation does not match that of **Down syndrome**, which is characterized by intellectual disability, characteristic facial features, and an increased risk of congenital heart defects. The mitten-hand sign is not a typical feature of Down syndrome.
* **Option B:** This option is incorrect because **Tuberous sclerosis complex** is a genetic disorder that is characterized by the development of benign tumors in multiple organs, including the skin, kidneys, and brain. While intellectual disability can occur in Tuberous sclerosis complex, the mitten-hand sign is not a characteristic feature of this condition.
* **Option C:** This option is incorrect because **Ehlers-Danlos syndrome** is a group of genetic disorders that affect the body's connective tissue, leading to skin hyperextensibility, joint hypermobility, and tissue fragility. While intellectual disability can occur in some types of Ehlers-Danlos syndrome, the mitten-hand sign is not a characteristic feature of this condition.

**Clinical Pearl / High-Yield Fact**
The mitten-hand sign is a characteristic physical examination finding in Fragile X syndrome. This sign is often seen in children with Fragile X syndrome who are between 2-5 years old, and it is essential to recognize this sign to make an early diagnosis of Fragile X syndrome.

**Correct Answer: C. Tuberous sclerosis complex.**