- #1

- 4,488

- 72

Just an idea.

which number is the next in sequence?

21, 34, 57, 61,.........

which number is the next in sequence?

21, 34, 57, 61,.........

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- Thread starter Andre
- Start date

- #1

- 4,488

- 72

Just an idea.

which number is the next in sequence?

21, 34, 57, 61,.........

which number is the next in sequence?

21, 34, 57, 61,.........

- #2

drizzle

Gold Member

- 379

- 57

24, 35??

Just a thought.

Just a thought.

- #3

- 4,488

- 72

Nice try, but no, the next one is perfectly logical and explainable, but there is a twist.

- #4

drizzle

Gold Member

- 379

- 57

How about; 93, 88, 129, 115?

- #5

- #6

- 4,488

- 72

Ambiguous twists actually :uhh:

- #7

I like Serena

Homework Helper

- 6,579

- 176

84?

Andre, this is too hard!

Andre, this is too hard!

- #8

- 4,488

- 72

You defeated your heuristic bias. Great job.

Can anybody else explain why?

- #9

- 4,488

- 72

- #10

- 103

- 1

Just an idea.

which number is the next in sequence?

21, 34, 57, 61,.........

There is no unique answer to these. It's a number based on

or the creator of the sequence (if not you).

You could be asking if we can figure out what rule/process you

happened to use.

- #11

- 4,488

- 72

The rule is...
that at least one of the lines of the left character/symbol is curved, twisted: 2,3,5,6,8,9,0 (the hint of the twist -used double-, ambigeously) while the right symbol is made of straight lines 1,4,7.

I wonder which other hidden -unintended- rules could exist. Can you give an example?

I wonder which other hidden -unintended- rules could exist. Can you give an example?

Last edited:

- #12

- 103

- 1

After starting out with 23,

it

add 1, add 2, add 1, add 2, etc. to the previous tens digit.

And for the subsequent units digits, they

cycling as 1, 4, 7, 1, 4, 7, etc.

[tex]Hence, \ \ \ 21, \ 34, \ 57, \ 61, \ \boxed{84}, \ ...[/tex]

As an aside, using my method, if I were to figure the next number

following 84, I would add 1 to 8 to get 9 for the tens digit,

and the units digit would be a 7 from the cycling as mentioned above.

[tex] \ ... , \ 84, \ 97, \ ...[/tex]

- #13

drizzle

Gold Member

- 379

- 57

21 → [2+1=3] And [21/7=3]

+13

34 → [3+4=7]

+23

57 → [5+7=12→1+2=3] And [57/3=19]

+4

61 → [3+4=7]

+23

84 → [8+4=12→1+2=3] And [84/7=12]

+13

97 → [3+4=7]

+23

12

+4

124 → [3+4=7]

+23

147 → [1+4+7=12→1+2=3] And [147/7=21]

+13

160 → [3+4=7]

+23

183

......

Rule: if the sum of all characters [digits] of the given number, results in 7 [keep adding the resultant digits until you end up with only one digit] then you add up 23 to the number to get the next in sequence. The other resultant number you may get other than 7, is 3. Here you'll have to add up 4 or 13 to the number. If that same number accepts the division by seven [it should result in an integer quotient] then you'd have to add 13 to get the following number. But if it accepts the division by three, then you add up 4 to the number. As you can see, you don't have to do this calculations all through, just figure the first next in sequence, and then add up 4 or 13 alternatively, of course with 23 in between.

You just can't do this intuitively.

- #14

- 1,045

- 2

-1, 2, 3, 8, 15, 24, 35, ...

Any takers?

Any takers?

- #15

I like Serena

Homework Helper

- 6,579

- 176

I got a better rule.

(snip)

You just can't do this intuitively.

That's... very twisted!! As requested by andre.

- #16

drizzle

Gold Member

- 379

- 57

That's... very twisted!! As requested by andre.

Well, couldn't come up with any convincing method other than this. :grumpy:

So, what's yours??

- #17

I like Serena

Homework Helper

- 6,579

- 176

Well, couldn't come up with any convincing method other than this.

So, what's yours??

Well, I was thinking of doing the twist.

So I was thinking left-right-left-right.

So I made 2 sequences from 21, 34, 57, 61.

21-57 and 34-61

First digit goes 3 up, second digit goes 6 up.

And since 4+6=10, summing those digits gives 1.

Next would be 57 + 36 -> (8)(7+6) -> (8)(13) -> 84!!!

To my surprise, andre was sure I had the right answer.

- #18

- 103

- 1

-1, 2, 3, 8, 15, 24, 35, ...

Any takers?

QuarkCharmer,

I would bet a lot that you have a typo, and that your

sequence should instead be:

-1,

In

entries are consecutive odd integers.

So 35 + 13 =

[tex]\boxed{48}[/tex]

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