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2 Kings 13:1 says that Jehoahaz began to reign in the 23rd year of Joash king of Judah and that he (Jehoahaz) reigned for 17 years. This means that Jehoahaz's reign ended in the 40th year of Joash's reign (ignoring rounding for now). 2 Kings 13:10 says that Jehoahaz's son, Jehoash, began to reign in the 37th year of Joash king of Judah. There seems to be a discrepancy of 3 years here; I can only account for this by saying that 23 was rounded up from 22, 17 was rounded up from 16, and 37 was rounded down from 38.

Any other ideas? Am I missing something?

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Most commentaries (actually all of them) that I looked up do not try and create an argument that would escape a copyists mistake in the manuscripts that are available to us today. It seems that it was quite easy to make a copyists mistake with Hebrew Numerals that would go undetected by other copyists due to the confusion of reckoning dates.

Here is one explanation of what it should possibly read.

This synchronistic statement is not only at variance with v. 10, but cannot be very well reconciled with 2 Kings 12:1. If Jehoahaz began to reign in the twenty-third year of Joash king of Judah, and reigned seventeen years, his son cannot have followed him after his death in the thirty-seventh year of Joash of Judah, as is stated in v. 10, for there are only fourteen years and possibly a few months between the twenty-third and thirty-seventh years of Joash; and even if he ascended the throne at the commencement of the twenty-third year of the reign of Joash and died at the end of the thirty-seventh, they could only be reckoned as fifteen and not as seventeen years. Moreover, according to 2 Kings 12:1, Joash of Judah began to reign in the seventh year of Jehu, and therefore Athaliah, who ascended the throne at the same time as Jehu, reigned fully six years. If, therefore, the first year of Joash of Judah coincides with the seventh year of Jehu, the twenty-eighth year of Jehu must correspond to the twenty-second year of Joash of Judah; and in this year of Joash not only did Jehu die, but his son Jehoahaz ascended the throne. Consequently we must substitute the twenty-second year of Joash, or perhaps, still more correctly, the twenty-first year (Josephus), for the twenty-third. If Jehu died in the earliest months of the twenty-eighth year of his reign, so that he only reigned twenty-seven years and one or two months, his death and his son’s ascent of the throne might fall even in the closing months of the twenty-first year of the reign of Joash of Judah. And from the twenty-first to the thirty-seventh year of Joash, Jehoahaz may have reigned sixteen years and a few months, and his reign be described as lasting seventeen years. (Keil, C. F., & Delitzsch, F. (1996). Commentary on the Old Testament (Vol. 3, p. 266). Peabody, MA: Hendrickson.)

Note: For those who believe in the infallibility of scripture as originally written, small mistakes like this do not cause us any discomfort. The miracle is that from human standards these cracks are so small and few.

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The Genesis commentary by Keil and Delitsch, though reprinted in English translation in 1996, was in fact written in 1861. It is doubtless still a valuable work, but it must be said that there has been some advance (perhaps not much) in Old-Testament studies in the last century and a half.

Specifically to this issue there is a well-known book by Edwin Thiele of which you can find a brief synopsis here:

http://en.wikipedia.org/wiki/The_Mysterious_Numbers_of_the_Hebrew_Kings

Thiele argues basically that the kingdoms of Judah and of Israel had different methods of calculating regnal years and that, with this assumption the Biblical data can be harmonized. Although not universally accepted, Thiele’s chronology has been supported by a good number of serious scholars.

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Whilst this may theoretically answer the question, it would be preferable to include the essential parts of the answer here (summarize the relevant portions of the resource that answer this question), and provide the link for reference. –  maj nem ɪz dæn Apr 22 at 21:25
    
Chris, I suggest you look up Thiele's book in a library. The argument is complicated and involves a lot of arithmetic. I personally am not convinced that his solution is necessarily correct, but it is a valiant attempt to vindicate the biblical text. –  fdb Apr 22 at 22:55
    
There are some useful summaries of recent chronologies available online (includes Thiele): that site also some further resources on the challenges of and approaches to the problems of biblical chronology. –  Davïd Apr 25 at 23:34

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