Discover the Rule
Found the following cute puzzle on Facebook.
Share:Puzzle. Discover the rule governing the following sequence to find the next term of the sequence: 8, 3, 4, 9, 3, 9, 8, 2, 4, 3.
Tanya Khovanova's Math Blog
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Alex:
6,7
31 December 2020, 8:55 pmBlaine:
…4,4,2,3,8
That was fun!
1 January 2021, 1:51 amgabriella:
…4,5,3,5,4,2,6,3,4,7,3,7,6,2,8,3,4,9…
1 January 2021, 6:28 amLeo B.:
…,1,9,5,2,4…
1 January 2021, 10:22 pmRobert:
… 4, 6, 3
but I’m not sure .. what is the reasoning behind?
2 January 2021, 5:37 amtanyakh:
One of the five answers above is correct. Hint: The rule is simple. If you are not sure, you didn’t discover it.
2 January 2021, 1:17 pmMichael:
Blaine has it. Unfortunately I don’t see a way to determine additional terms… unless they are 1, 1, 1…?
3 January 2021, 4:06 pmBlaine:
Michael, perhaps it could continue as 5, 5, 4, 4, 5, 4, 5, 3… and would it eventually devolve into 4, 4, 4… ?
4 January 2021, 10:19 amRichard:
Mmmh, I don’t follow
6 January 2021, 5:10 amtanyakh:
Hint: This is a self-referencing puzzle.
6 January 2021, 2:47 pmLeo B.:
I got it; however, my very simple (and human language-independent!) program says 1,9,5,2,4.
Indeed, the rational number with the lowest denominator, which decimal form starts with .8349398243 is 138681/166097 = 0.83493982431952413348…
7 January 2021, 1:47 amStefano:
…4,4,2,3,9(or 8) ?
9 January 2021, 12:23 pmCristóbal Camarero:
I see the mirror rule a(i)=a(13-i)+1 for i<13-i, i!=4. This would continue with two terms: 2 and 7. But this is different to all given ones and Tanya said the good is already given.
25 January 2021, 7:29 amBlaine:
Hint: ignore the word “Puzzle” and proceed from there.
8 February 2021, 12:56 amCristóbal Camarero:
Oh! I see now, nice. Not as much a self-referencing puzzle as a prelude-referencing one, I would say.
8 February 2021, 4:42 pmMarnix:
…8
And perhaps a couple of 1’s if you’re so inclined 🙂
10 February 2021, 4:29 amMarnix:
..4, 4, 2, 3, 8.
And perhaps a couple of 1’s if you’re so inclined… 🙂
10 February 2021, 4:31 amPer:
Meh, its not in the OEIS, so most likely not given by some easy formula…
7 May 2021, 4:55 pmTaposik:
This is fun, I am sure the next few terms according to this rule would be 4, 2, 3, 1, 2, 4, 3 , 4, 3, 5, 9
8 July 2021, 2:09 am