# How can the 3 Questions be resolved with the math still correct?

Analyzing Noah and the Great Flood story, there appear to be 3 math problems, each with its own set of factors and calculations, that aren’t easy to resolve.

First is the “2 years after the flood” problem; in combining three specific verses and checking the math there end ups being a 2 year difference to explain.

Gen 5:32: And Noah was 500 hundred years old: and Noah begat Shem, Ham, and Japheth.

Gen 7:11 In the 600th year of Noah's life, in the 2nd month, the 17th day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened.

Gen 11:10 These are the generations of Shem: Shem was 100 years old, and begat Arphaxad, 2 years after the flood. (KJV).

Q#1: How could Shem have become a father 2 years after the flood?

Second, it’s hard to determine if Shem’s son Arphaxad was born on the ark or not. This leaves another difference to resolve.

Q#2: Was or wasn’t Shem’s son Arphaxad born on the ark? (See the link).

Finally, starting with additional factors from the end of Noah’s life and moving backwards there’s yet a third problem to resolve. It doesn't seem Noah could have lived as long as he did yet be only 500 years older than Shem.

Gen 9:28-29 And Noah lived after the flood 350 years. And all the days of Noah were 950 years: and he died.

Gen 5:32: And Noah was 500 hundred years old: and Noah begat Shem, Ham, and Japheth.

Gen 7:11 In the 600th year of Noah's life, in the 2nd month, on the 17th day of the month, the same day were all the fountains for the great deep broken up, and the windows of heaven opened. (KJV)

Here, based on Gen 9:28-29 it seems Noah was probably 600 years after the flood (950-350) and Shem was probably 100 at that time (Noah’s 600 less Shem being 500 years younger). However, Shem could have been neither 100 (when he became a father per Gen 11:10) nor even 99 years old when the floodgates were opened. The flood lasted more than 1 year, and no living child entered or left the ark.

Q#3: How could Noah have lived to be 950 years old?

Summary Question: How can the 3 questions/problems above be resolved with the math still correct?

• All these numbers are nice round numbers. Can we not assume it was meant "about 600 years"?
– user3638
Mar 5 '14 at 13:56
• @DarkHeart I don't believe we're supposed to round these particular figures, especially since the detail takes the time of events to even the day. I think there's a message within the math of this. Soldarnal sort of addressed this being so interesting via a question he had hermeneutics.stackexchange.com/q/4672/2873 Mar 6 '14 at 2:31
• Can't the word "begat" have been referring to the time of conception or birth of the First of the brothers? May 17 '14 at 19:46
• Sep 4 '20 at 12:55
• @Lucian Are you just suggesting I consider inclusive counting? or does it present a different answer (i.e. their ages didn't change). Dec 19 '20 at 21:00

These 3 enigmas or problems can only be solved if fatherhood and childhood (life) are calculated from conception forward. Otherwise the math won't work.

The 3 problems above require certain information in order to reach 2 key facts. Then the math issues can be resolved.

• Who entered and who left the ark?
• How long did the flood last? (How long was Noah on the ark such that everyone’s age went up?)

The information for these makes the answers unquestionable.

### Fact #1

Clearly only Noah, his wife, his 3 sons and his sons’ wives entered and left the ark.

Entering the ark (per the KJV):

Gen 6:10 And Noah begat three sons, Shem, Ham, and Japheth.

Gen 6:18 But with thee will I establish my covenant; and thou shalt come into the ark, thou, and thy sons, and thy wife, and thy sons' wives with thee.

Gen 7:6-7 And Noah was six hundred years old when the flood of waters was upon the earth. And Noah went in, and his sons, and his wife, and his sons' wives with him, into the ark, because of the waters of the flood.

Gen 7:13 In the selfsame day entered Noah, and Shem, and Ham, and Japheth, the sons of Noah, and Noah's wife, and the three wives of his sons with them, into the ark.

Leaving the ark (KJV):

Gen 8:15-17 And God spake unto Noah, saying, Go forth of the ark, thou, and thy wife, and thy sons, and thy sons' wives with thee. Bring forth with thee every living thing that is with thee, of all flesh, both of fowl, and of cattle, and of every creeping thing that creepeth upon the earth; that they may breed abundantly in the earth, and be fruitful, and multiply upon the earth.

Gen 8:18-19 And Noah went forth, and his sons, and his wife, and his sons' wives with him: Every beast, every creeping thing, and every fowl, and whatsoever creepeth upon the earth, after their kinds, went forth out of the ark.

Gen 9:1 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.

Gen 9:8-9 And God spake unto Noah, and to his sons with him, saying, And I, behold, I establish my covenant with you, and with your seed after you;

Gen 9:18-19 And the sons of Noah, that went forth of the ark, were Shem, and Ham, and Japheth: and Ham is the father of Canaan. These are the three sons of Noah: and of them was the whole earth overspread.

### Fact #2

The span of time between when the floodgates were opened and the earth was again dry (or Noah and his adult relatives could have left the ark) was more than 1 year. Therefore everyone’s age went up.

### Exact Flood Extent = 1 year and 10 days (or about 375 days):

In the 600th year of Noah's life, in the 2nd month, on the 17th day of the month…the floodgates of the sky were opened. (Gen 7:11)

In the 601st year of Noah's life…in the 2nd month, on the 27th day of the month…the earth was dry. (Gen 8:13-14)

The time between those 2 verses is exactly 1 year, 10 days (or about 375 days).

### Estimate of Flood Extent (374 days):

• A- The floodgates of the sky were opened.

“The waters maintained their crest over the earth for 150 days, and then God remembered Noah and all the animals, wild and tame, that were with him in the ark. So God made a wind sweep over the earth, and the waters began to subside. The fountains of the abyss and the floodgates of the sky were closed, and the downpour from the sky was held back” (Gen 7:24 – 8:2).

• C- Add another 150 days:

“Gradually the waters receded from the earth. At the end of 150 days, the waters had so diminished that, in the 7th month, on the 17th day of the month, the ark came to rest on the mountains of Ararat” (Gen 8:3-4).

“The waters continued to diminish until the 10th month, and on the 1st day of the 10th month the tops of the mountains appeared” (Gen 8:5).

The net time between Gen 8:5 and Gen 8:4 just before it is about 74 days. (Gen 8:5 having had 9 months gone by less: Gen 8:4 having had 6 months and 16 days having passed. That difference is 2 months and about 14 days. 2 months * 30 days/month + 14 days = 74 days).

The total for this estimate is therefore 374 days (150 + 150 + 74).

### Estimate of when Noah left the Ark (381 days):

• A- The floodgates of the sky were opened.

“The waters continued to diminish until the 10th month, and on 1st day of the 10th month the tops of the mountains appeared” (Gen 8:5).

With 9 months having passed, this is about 270 days (9 months * 30 days/month).

“At the end of 40 days Noah opened the hatch he had made in the ark, and he sent out a raven, to see if the waters had lessened on the earth. It flew back and forth until the waters dried off from the earth. Then he sent a dove to see if but the dove could find no place to alight and perch, and it returned to him in the ark, for there was all over the earth. Putting out his hand, he caught the dove and drew it back to him inside the ark” (Gen 8:6-9).

“He waited 7 days more and again sent out the dove out from the ark. In the evening the dove came back to him, and there in its bill was a plucked-off olive leaf! So Noah knew that the waters had lessened on the earth.” (Gen 8:10-11)

• E- Add another 7 days:

“He waited still another 7 days and then released the dove once more; this time it did not come back.” (Gen 8:12)

The additional time, from Gen 8:13 to when the earth was dry at Gen 8:14, was about 57 days.

“In the 601st year of Noah’s life, in the 1st month, on the 1st day of the month, the water began to dry up on the land. Noah then removed the covering of the ark and saw that the surface of the ground was drying up.”(Gen 8:13)

“In the 2nd month, on the 27th day of the month, the earth was dry.” (Gen 8:14)

Regarding the 601st year of Noah’s life, Gen 8:13 is in the 1st month’s 1st day; Gen 8:-4 is in the 2nd month’s 27th day. The difference between the two is about 57 days.

The total for this estimate is therefore 381 days (270 + 40 + 7 + 7 + 57).

Theologians such as Professor Gerhard von Rad and Jeremy Hughes haven’t been able to explain the issues; they focused on the 2 year flood problem.

Professor Gerhard von Rad per his book "Genesis":

“There is an inconsistency between the data in Ch. 5-32 and Ch. 7-11 on the one hand and Ch. 11.10 on the other which has not yet been satisfactorily solved, if one decides against simply deleting the words “two years after the flood”, for at this time Shem was not 100 years old, but 102.”

Jeremy Hughes per his Secrets of the Times:

“And the only way out of this dilemma that I can see is to suppose that this 2 year interval is actually a chronological correction made after 2 years had fallen out of antediluvian chronology through some process of textual corruption when it was noticed that the remaining figures no longer added up to the correct totals required by Priestly tradition.”

## Conclusion

We’ve been misinterpreting the wording of these problems and therefore finding our math incorrect. In every case, the Genesis authors are telling us that "years old" (KJV) and "years old"/"age"/“lifetime” (NAV) begin at birth. However, they're also saying, mathematically, that parenthood and childhood/"life" can only begin at conception. Thinking in that way the math gets resolved; otherwise it does not. The best example for showing this is the most difficult problem, the "2 years after the flood":

Note: Calculations below use 30 days in a month, 9 months of time between conception and birth, and “age” meaning “years old”.

Gen 5:32: And Noah was 500 hundred years old: and Noah begat Shem, Ham, and Japheth. (KJV)

Noah became Shem’s father at conception, but Shem wouldn’t be born for about 9 more months. 9 months after Shem’s conception, Noah would have been at least 500 years, 9 months old and at most 501 years, 8 months, 29 days old (the latter being 9 months added to 500 years, 11 months, 29 days old).

Gen 7:11 In the 600th year of Noah's life, in the 2nd month, the 17th day of the month, the same day were all the fountains of the great deep broken up, and the windows of heaven were opened. (KJV)

Noah’s life to date, in its 600th year, 2nd month, 17th day would have been 599 years, 1 month, 16 days. With his conception having been 9 months earlier, deducting 9 months from that would have his age at 598 years, 4 months, 16 days.
Therefore, Shem’s age at the start of the flood would have been at least 96 years, 7 months, 17 days and at most 97 years, 7 months, 16 days. (i.e. Noah’s specific age at the start less how much Noah may have been older).

Gen 11:10 These are the generations of Shem: Shem was 100 years old, and begat Arphaxad, 2 years after the flood. (KJV).

At the end of the flood which lasted 1 year, 10 days, Shem’s age would have been at least 97 years, 7 months, 27 days, and at most 98 years, 7 months, 26 days.*

2 years later, and in terms of years only, Shem could have been 100 years old and able to begat his son, with the math correct and no child having left the ark. Only this works.

* Those are the range of his ages at the start of the flood with the stretch of the flood added).

Two stories, one from Luke and the other from Genesis, show children alive in mothers' wombs.

• Luke shows the baby John in Elizabeth’s womb leaping for joy, and a pregnancy lasting about 9 months.

“And it came to pass, that, when Elisabeth heard the salutation of Mary, the babe leaped in her womb, and Elisabeth was filled with the Holy Ghost (Luke 1:41); “For, lo, as soon as the voice of thy salutation sounded in mine ears, the babe leaped in my womb for joy.” (Luke 1:44) “And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the 6th month with her, who was called barren. For with God nothing shall be impossible.” (Luke 1:36-37) “And Mary abode with her about 3 months, and returned to her own house.” (Luke 1:56) (KJV)

• Genesis has the babies Esau and Jacob fighting while in, after leaving, and while being born from Rebekah’s womb, with Jacob holding Esau’s heels. God confirms the “two nations (are) in thy womb” are the twins struggling.

“And the children struggled together within her; and she said, If it be so, why am I thus? And she went to enquire of the LORD. And the LORD said unto her, Two nations are in thy womb, and two manner of people shall be separated from thy bowels;” (Gen 25:22-23) (KJV) “And the first came out red, all over like an hairy garment; and they called his name Esau. And after that came his brother out, and his hand took hold on Esau's heel; and his name was called Jacob: (Gen 25:25-26) (KJV)

In summary, the two stories’ words show children’s action/life in mothers’ wombs. The Genesis authors, in using the numbers/ages, take the assumption that parenthood and childhood/"life" begin at conception and reveal it to be a fact.

Supplemental notes:

1. Two of several signs I found came from focusing on parenthood years for everyone we can in Genesis, including Sarah, the only female in Scripture with any age given. That total came to 9,999, yet only under the assumption that parenthood begins at conception. Next, the total parenthood years after the flood turned out to be 3,333, but again only under the same key assumption. While these truly prove nothing on their own, they became great signs toward reaching the conclusion with math correct.

2. From these 3 cases fatherhood begins at conception, so motherhood and childhood/life have to also. Furthermore, that helps explain the following questions.

• I just want to warn you of something. How many days in the Jewish year, which Moses wrote? The number of days in the Hebrew calendar has not always been the same. Furthermore, your answer is excellent. Feb 20 '14 at 21:48
• @PaulVargas Since Moses was allegedly raised as an adopted member of the Egyptian royal family, it seems reasonable to conclude that the Egyptian calendar systems would be what Moses was most familiar with. Feb 24 '14 at 16:55
• Actually, along with seeing no children left the ark, what's most important is that Noah's age went up. That's the base for the math. Thanks. icr.org/article/calendar-antiquity-genesis Feb 24 '14 at 21:17
• @DavidH Numbers were used for the months throughout the Pentateuch. The names of the months were after the Babylonian captivity. Interestingly, one of the Egyptian lunar calendars is very similar to the Hebrew lunar calendar. Feb 26 '14 at 5:02
• The verb y-l-d means both “to beget” (of a man) and “to give birth” (of a woman); you can read this in any Hebrew dictionary. But there is no evidence that the Hebrews, or any of the Semitic peoples, counted a person’s age from his or her conception. They counted from the moment of birth.
– fdb
Mar 3 '14 at 15:47

Below are charts to help visually facilitate understanding of this enigma in exploration of various solutions:

One difficulty that must be addressed is that Genesis 7:6 says, "Noah was six hundred years old when the floodwaters were on the earth." If this is taken chronologically then the phrase in the 600th year of Noah's life cannot refer to the year prior, but must refer to the year following his 600th birthday.

``````CHART 1
``````

-This chart depicts the days/months given in the flood account as those of the calendar year (not of Noah's life).
-This chart is based on the traditional understanding with years old and years of life synonymous and calculated from birth.
-This chart sees "in the 600th year of Noah's life" = on or before Noah's 600th birthday. But avoids disrupting the chronology as follows: The only one day on which Noah would be both 600 and in his 600th year of life would be his 600th birthday. Thus the flood would have begun on his 600th birthday, in the 2nd month of the calendar year.

The difficulty here is that, in order for Arphaxad to be born two years after the flood he would have to be born on or after Noah's 602nd birthday which falls outside of the range in which Shem could have been 100years old based on the dates given for Shem's birth.

``````CHART 2
``````

-This chart views Genesis 7:6 as not chronological account. It sees in the 600th year of Noah's life, as the year before his 600th birthday (like a child is in their first year during the year prior to their first birthday).
-This depicts days/months given in the flood account as of Noah's life (rather than of the calendar year).
-This chart is based on the traditional view that years old and years of life are synonymous and are calculated from birth.

So, say Shem was born just prior to Noah's 501st birthday: Shem would turn 100 years old just prior to Noah's 601st birthday. Shem would be still 100 years old from just prior to Noah's 601st birthday to just prior to his 602nd birthday.

Thus, Arphaxad could be born at any time between Noah's 600th and 602nd birthday Thus, two years after the flood begins falls in the time frame in which Aprhaxad could be born! (See the yellow circle where the two lines intersect.)

This works, but the "Chronology is disrupted" However, it is worth noting that if Genesis 7:6 were chronological then the floodwaters would be on the earth before Noah and his family are on the ark as depticted by the verses following (Gen 7:7-9).

This chart works except the chronology of Gen 7:6 and 7:11 is disrupted same as in chart 2.

Noah was six hundred years old when the floodwaters were on the earth. So Noah, with his sons, his wife, and his sons' wives, went into the ark because of the waters of the flood. Of clean animals, of animals that are unclean, of birds, and of everything that creeps on the earth, two by two they went into the ark to Noah, male and female, as God had commanded Noah. And it came to pass after seven days that the waters of the flood were on the earth. In the six hundredth year of Noah's life, in the second month, the seventeenth day of the month, on that day all the fountains of the great deep were broken up, and the windows of heaven were opened. And the rain was on the earth forty days and forty nights.

`````` Chart 3
``````

-This chart is from fdb's perspective/explanation.
-In 600th year of life = the year before turning 600 years old
-day and month = of the calendar year

If you look at the exact wording it is all very simple.

Gen 5:32 says that Noah begat Shem, Ham and Japheth at the age of 500 years (Hebrew: “the son of 500 years“). If he begat three sons in the same year he must have had at least two wives at that time, but let us leave that out of consideration. Let us assume that Noah was born on the first day of the year and that he begat Shem on his 500th birthday. Shem would then have been born when Noah was 500 years and 9 months old.

Gen 7:11 says that the flood began “in Noah’s 600th year” - that means: in the year ending with his 600th birthday, when he was 599 - month 2, day 17. This is about 7 months before Shem’s 99th birthday (still assuming that Noah begat him on his 500th birthday). So at the beginning of the flood Shem was 98 years old. This means that on the first anniversary of the beginning of the flood Shem was 99, and on the second anniversary he was 100. This is consistent with the statement in Gen 11:10 that Shem was “the son of 100 years” two years after the flood.

• "Month 2, day 17" refers to the 17th day of the 2nd month of the year, of whatever calendar was used by the author of Genesis. To simplify the arthmetic I have assumed that Noah was born on the first day of the year. My intention was merely to prove that the numbers in the text are arithmetically possible, not to determine the exact date of Shem's birth.
– fdb
Mar 13 '14 at 14:34
• I have to disagree that "If he begat three sons in the same year he must have had at least two wives at the time." He could have, but the account only mentions one wife. However, it is also just as easily possible the boys were a set of triplets, or two were a set of twins (fraternal or identical). Two wives is in no way demanded by this fact. Mar 20 '14 at 16:30
• @fdb With that working from an assumption, couldn't the results change if the assumption were changed, even though he was still 500? Mar 21 '14 at 21:57
• fdb. You said, "Let us assume that Noah was born on the first day of the year and that he begat Shem on his 500th birthday. Shem would then have been born when Noah was 500 years and 9 months old." It sounds like you are saying here that begat means conception and thus at 500, 9mo Shem would be born. Do you think yelad = birth or conception?
– user2027
Mar 24 '14 at 15:01
• As I wrote further up the page: The verb y-l-d means both “to beget” (of a man) and “to give birth” (of a woman).
– fdb
Mar 24 '14 at 16:33

Notational convention for this response

Dates will be stated as year.month.day, where year is AM if only the year number is stated or the nth year in the life of a person if the year is stated as name.n. Thus, the day when the Flood began is 1656.2.17 = Noah.600.2.17. Also, month.day may be replaced by d.nnn, with nnn being the day number within the year, so the previous date is also 1656.d.047 = Noah.600.d.047.

The first year after Creation is year 1. You are n years old (yo) in the (n+1)th year of your life.

Chronological framework for the first three biblical patriarchs

1 AM (after d.006) = Adam's 1st year, when he was 0 yo.

...

131.1.6: Adam turned 130 yo. At this moment, he had lived 130 years.

131 AM (after d.006) = Adam's 131st year, when he was 130 yo.

When Adam was 130 yo he begot Seth. So Seth was born in the year 131 AM. Let us assume that it was precisely on Adam's birthday. Thus:

131 AM (after d.006) = Seth's 1st year, when he was 0 yo.

132.1.6: Seth turned 1 yo.

...

236.1.6: Seth turned 105 yo. At this moment, he had lived 105 years.

When Seth was 105 yo he begot Enosh. So Enosh was born in the year 236 AM.

...

The point of this is to show that, if the sum of the begetting ages of the previous patriarchs is n, a patriarch was born, at the earliest, in the year (n + 1) AM. Thus, assuming that all patriarchs up to Lamech begot their first sons on their birthdays, Noah was born in 1057.1.6, so that 1057 AM is the 1st year of Noah's life.

Chronological framework for Noah and Shem

1057, Noah.1, Noah was 0 yo.

...

1557, Noah.501, Noah was 500 yo.

• 1557.sm.sd: Noah begot Shem (Gen 5:32), with sm.sd > 2.27.

...

1656, Noah.600, Noah was 599 yo.

• 1656.2.17: Flood began.

1657, Noah.601, Noah was 600 yo.

• 1657.2.27: the earth was dry; Noah and his famility leave the ark.

• 1657.sm.sd: Shem turned 100 yo, with sm.sd > 2.27.

1658, Noah.602, Noah was 601 yo.

• 1658.2.17: Shem begot Arpachshad, exactly 2 years after the Flood began (Gen 11:10).

• 1658.sm.sd: Shem turned 101 yo, with sm.sd > 2.27.

While the statement by the P author that "Shem was a hundred years old, and begot Arpachshad two years after the flood." (Gen 11:10) does not mean necessarily that Arpachshad was born exactly two years after the Flood began, it is clear that the data item "two years after the flood" was provided by the P author to ensure that the Flood chronology was understood correctly as stated above.

Thus, the answer to Q#1 has been provided above, the answer to Q#2 is "No, Arpachshad was definitely not born or even conceived on the ark.", and the answer to Q#3 has also been provided above: assuming that all patriarchs up to Lamech begot their first sons on their birthdays, Noah was born in 1057.1.6, turned 600 yo on 1657.1.6, a few days after 1657.1.1, when "the water was dried up from the earth" (Gen 8:13), and turned 950 yo on 2007.1.6, having lived 950 years up to that moment. Therefore:

• the years of Noah's life up to, and including, the year of the Flood were 600: 1057..1656;

• the years of Noah's life after the year of the Flood were 350: 1657..2006.