Genesis 5:32 says that Noah was 500 when he begat Shem, Ham, and Japheth. Genesis 7:11 says that the Flood started in Noah’s 600th year. Genesis 8:13 says the Flood waters completely receded in Noah’s 601st year (around 10 and a half months after it started). And Genesis 11:10 says that Shem begat Arphaxad two years after the Flood when he was 100 years old. Now, the math doesn’t add up because if the Flood ended in Noah’s 601st year, Shem should have been 103 (or 102 if the beginning of the Flood is counted though that’s unlikely).
The answer to this riddle is that Shem is not the firstborn. Although he’s listed first, this doesn’t have a definitive say on who was born first. For example, in Genesis 5:32 Ham is listed second, but in Genesis 9:24 we see that he was the youngest. Therefore, the lists that place Shem first (and Ham second), do so because of his notoriety (as the ancestor of the Semites/Israelites) and Ham’s second place is because of his ancestry of Canaan, which was Israel’s number 1 enemy at the time of Moses (until the advent of the Philistines). From Genesis 10:21 we learn that Japheth was the older brother of Shem. The Hebrew of Genesis 10:21 which literally reads more or less: “Unto Shem also, the father of all the children of Eber, the brother of Japheth the elder, even to him were children born.” (KJV) and it’s easiest to interpret that Japheth was the eldest brother of the three, which would make Shem the middle child
Now the statement in Genesis 5:32 that Noah was 500 when he begat the three sons does not mean that all 3 were born when he was 500 (or else Ham would not be the youngest), but that the first was born when he was 500 – Japheth. Then it would have been Shem (when Noah was 502/3 and Ham). The difference of 2-3 years between Japheth and Shem might seem very small compared to the whole lifespan of Noah. However, we can be assured that Noah probably had children before he turned 500 and that the three sons (and their wives) that he had with him on the Ark were the ones that were living with/near him and this would make sense for the 100 years prior to the Flood, for Japheth, Shem and Ham to have been born within those 100 years (which Genesis 5:32 confirms). From there, whether the difference is 20-30 or 2-3 years between the births of Japheth and Shem, I don’t see much of a coincidence – that’s just how it happened. Therefore, we probably don’t have a copyist error here, nor a contradiction.
