# Important days in history… and to come!

The other day I decided I wanted to come up with another simple puzzle before releasing another toughy on puzzling.SE. I came across an interesting series of dates that I wanted to share and see if people could figure out what the next date in the series was.

The series of dates is:

     March 30, 1973
April 1, 1975
June 28, 1978
September 27, 1983
March 24, 1992
December 18, 2005
............., .....


What is the next date in the series? Explain.

• The third date (1992) lies exactly in the middle between the first date (1978) and the fourth date (2005). – Gamow Mar 24 '16 at 16:45
• Well. Apparently I'm getting downvotes on this one because people can't figure it out? @Gamow give it a go. Some people have been on the right track, just not quite using it properly. – Z. Dailey Mar 24 '16 at 16:48
• I have already spent a lot of time thinking about it, and I do not recognize the pattern. Could you perhaps give us the date that precedes June-28-1978? – Gamow Mar 24 '16 at 16:59
• Added 2 preceding dates... no point it having it closed down by people that are mad they were wrong and are too proud to ask for another hint... If my problems are unsolvable I always add hints as necessary. – Z. Dailey Mar 24 '16 at 17:03
• The dates actually have a special property. As hinted by the tags. It's likely a math property. @question_asker and originally I had a brain teaser tag on it because it's not immediately obvious but one little thing will reveal the whole answer. – Z. Dailey Mar 24 '16 at 17:06

I would guess that the answer is

March 10, 2028

Argument:

Whenever I look at four consecutive dates $d_1,d_2,d_3,d_4$ in this sequence, then the third date is exactly in the middle between the first date and the fourth date; mathematically, this means $d_3=(d_1+d_4)/2$.

(Thanks to Z Dailey): The Unix timestamps of these dates are the Fibonacci numbers.

• This answer is correct, but there's another famous pattern that contains the same traits. And there's a slightly nerdier way of generating the dates. A little more UNIX-related. I'll give the check but if you'd like to think on it a minute. – Z. Dailey Mar 24 '16 at 17:27
• rot13 gvzrfgnzc(svobanppv(a)) – Z. Dailey Mar 24 '16 at 17:41
• Unbelievable. Great puzzle! I should have recognized the underlying recursion. – Gamow Mar 24 '16 at 17:44
• Yah, If you can add that to your answer so people can view it a little easier (as you got the checkmark.) I don't know why so many people have downvoted it though... If you don't like math problems and patterns, don't click on one.... – Z. Dailey Mar 24 '16 at 17:45

My guess is

December 8, 2022.

Reasoning:

Treat each datepart (month, day, year) independently, and look at the difference between subsequent dates.
For months, the difference increases by three each time (June to September is 3 months, September to March is 6, March to December is 9). So the next step is to add 12 months, putting us back in December.
For day, the differences are 1, 3, 6, which are triangle numbers. Subtracting the next triangle number (10) gives 8.
For year, the differences are 5, 9, 13. These increase by four each time, so to get the last year, we add 17, giving 2022.

• Not quite. Have another go at it. – Z. Dailey Mar 23 '16 at 19:51
• Scott's answer solves your puzzle and is perfectly good!! The OEIS knows 322 number sequences with 5-9-13 oeis.org/search?q=5%2C+9%2C+13 Your puzzle text does not give information which of these 322 sequences you would like to see as an answer. The right answer only exists in your head but not in the puzzle text. Downvote. – Haobin Mar 24 '16 at 9:26

My guess is:

December 8, 2027

My reasoning:

Very similar to ScottM's, but not wrapping around within the same year:

The month difference increases linearly by threes (3, 6, 9), the day difference decreases triangularly (-1, -3, -6), and the year difference increases fibonaccily (5, 8, 13).

Specifically, there is an 8-year difference between 1983 and 1992 after you take into account that the 6-month difference (between Sept and March) spanned a year boundary.

So, the gap from the last given date will be +21 years, +12 months, -10 days, which simplifies to +22 years, -10 days.

• In the ballpark, but not quite. – Z. Dailey Mar 23 '16 at 22:28

March 10,2028(Thanks @Gamow)

The difference in the dates follows a Fibonacci pattern.

For example,difference between March $30,1973$ and April $1,1975$ is $2$ years $2$ days.
Difference between between April $1,1975$ and June $28,1978$ is $3$ years $2$ months $27$ days.
Difference between June 28,1978 and September 27,1983 is $5(=2+3)$ years $2(=0+2)$ months $29(=27+2)$ days and so on.

Moreover for any Fibonacci series,we have

$f_n$ $+$ $f_{n+3}$ = 2$f_{n+2}$, which supports @Gamow's claim.

• That is a pattern that should work, but check my comment on Gamow's answer... I fear the real answer is far more sinister. – Z. Dailey Mar 24 '16 at 17:47

My Guess is:

Thursday, 9 March 2028

My Reason is:

The numbers of days between the previous two dates combined equates to the ! next date - 1 (I'm not sure why the - 1)
Number of days between June 28 1978 and September 27 1983 is 1917
Number of days between September 27 1983 and March 24 1992 is 3101
Number of days between March 24 1992 and December 18 2005 is 5017
1917 + 3101 - 1 = 5017
3101 + 5017 - 1 = 8117
December 18, 2005 + 8117 days is Thursday 9 March 2028

• I think you meant to write 5017 both times, not 5107. :-) – Hellion Mar 24 '16 at 15:05
• This answer is slightly off. – Z. Dailey Mar 24 '16 at 16:20
• @Z.Dailey this still fits with the new dates - But obviously I'm missing something – Drifter104 Mar 24 '16 at 17:35
• So is Gamow, but he happened to get the right answer and his will continue to work throughout the pattern. This was extremely close!!! – Z. Dailey Mar 24 '16 at 17:38
• @Z.Dailey ah hadn't seen that - Now I get it – Drifter104 Mar 24 '16 at 17:42