**Core Concept**
Duodenal blowout, also known as duodenal stump blowout or postoperative duodenal stump rupture, is a rare but potentially life-threatening complication that can occur after a Whipple procedure or other surgeries involving the duodenum. It is characterized by leakage from the duodenal stump, leading to peritonitis and sepsis.

**Why the Correct Answer is Right**
The duodenal blowout typically occurs on the 5th to 7th postoperative day due to the delayed healing of the duodenal stump. This is because the duodenum has a high concentration of pancreatic enzymes, which can interfere with the healing process. The duodenal stump is also subject to increased pressure from the surrounding tissues, which can contribute to the rupture. The delayed occurrence of duodenal blowout is often a result of the body's initial response to the surgery, which involves the release of various enzymes and hormones that can delay healing.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because duodenal blowout is not typically seen on the 1st postoperative day, as the body has not yet fully responded to the surgery and the duodenum has not yet begun to produce high levels of pancreatic enzymes.
* **Option B:** This option is incorrect because duodenal blowout is not typically seen on the 10th postoperative day, as the duodenal stump would have had sufficient time to heal by this point.
* **Option C:** This option is incorrect because duodenal blowout is not typically seen on the 3rd postoperative day, as the body is still in the early stages of healing and the duodenum has not yet begun to produce high levels of pancreatic enzymes.

**Clinical Pearl / High-Yield Fact**
A key factor in the development of duodenal blowout is the delayed healing of the duodenal stump, which can be influenced by the high concentration of pancreatic enzymes in the duodenum. Surgeons should be aware of this risk factor and take steps to prevent it, such as using a mental closure technique or applying a duodenal stump closure device.

**Correct Answer:** C.