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Number Sequences

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Number Sequences - Back to the Number Puzzles

There are infinite formulas that will fit any finite series. Try to guess the following number in each sequence (using the most simple mathematical operations, because as I mentioned, there is more than one solution for each number sequence).

* 8723, 3872, 2387, ?

* 1, 4, 9, 18, 35, ?

* 23, 45, 89, 177, ?

* 7, 5, 8, 4, 9, 3, ?

* 11, 19, 14, 22, 17, 25, ?

* 3, 8, 15, 24, 35, ?

* 2, 4, 5, 10, 12, 24, 27, ?

* 1, 3, 4, 7, 11, 18, ?

* 99, 92, 86, 81, 77, ?

* 0, 4, 2, 6, 4, 8, ?

* 1, 2, 2, 4, 8, 11, 33, ?

* 1, 2, 6, 24, 120, ?

* 1, 2, 3, 6, 11, 20, 37, ?

* 5, 7, 12, 19, 31, 50, ?

* 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, ?

* 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ?

* 4, 7, 15, 29, 59, 117, ?

* 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, ?

* 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, ?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

Pls visit New Puzzles section to see always fresh brain teasers.

Number Series - solution

• 8723, 3872, 2387, ? 7238 (moving of numerals)

• 1, 4, 9, 18, 35, ? 68 (x*2+2, +1, +0, -1, -2)

• 23, 45, 89, 177, ? 353 (x*2-1)

• 7, 5, 8, 4, 9, 3, ? 10, 2 (two series – every second number: 7, 8, 9, 10 and 5, 4, 3, 2)

• 11, 19, 14, 22, 17, 25, ? 20, 28 (two series – every second number: 11, 14, 17, 20 and 19, 22, 25, 28)

• 3, 8, 15, 24, 35, ? 48 (x+5, +7, +9, +11, +13)

• 2, 4, 5, 10, 12, 24, 27, ? 54, 58 (x*2, +1, *2, +2, *2, +3, *2, +4)

• 1, 3, 4, 7, 11, 18, ? 29 (a+b=c, b+c=d, c+d=e …)

• 99, 92, 86, 81, 77, ? 74 (x-7, -6, -5, -4, -3)

• 0, 4, 2, 6, 4, 8, ? 6 (x+4, -2, +4, -2, +4, -2)

• 1, 2, 2, 4, 8, 11, 33, ?

• 1, 2, 6, 24, 120, ? 720 (x*2, *3, *4, *5, *6)

• 1, 2, 3, 6, 11, 20, 37, ?

• 5, 7, 12, 19, 31, 50, ? 81 (a+b=c, b+c=d, c+d=e …)

• 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, ? 322, 161 (x*3+1, /2, *3+1, /2 …)

• 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ? 485, 1456 (x/2, *3+1, /2, *3+1 …)

• 4, 7, 15, 29, 59, 117, ? 235 (x*2-1, *2+1, *2-1 …)

• 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, ? 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5

• 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, ? 4, 4

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• 4 weeks later...

• 1, 2, 2, 4, 8, 11, 33, ?

1 + 1 = 2

2 * 1 = 2

2 + 2 = 4

4 * 2 = 8

8 + 3 = 11

8 * 3 = 33

33 + 4 = 47

47 * 4 = 188

...

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1, 2, 3, 6, 11, 20, 37, ?

i dont know about the change between 1 & 2 but

it is the # + the two previous numbers

2+1+0=3

3+2+1=6

6+3+2=11

11+6+3=20

20+11+6=37

37+20+11=68

?=68

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• 4 weeks later...

27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, ? 322, 161 (x*3+1, /2, *3+1, /2 …)

27 * 3 + 1 = 82

82 / 2 = 41

41 * 3 + 1 = 124

124 / 2 = 62

62 * 3 + 1 = 187

real formula should be:

Odd numbers: *3+1

Even numbers: /2

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• 4 weeks later...
1, 2, 3, 6, 11, 20, 37, ?

i dont know about the change between 1 & 2 but

it is the # + the two previous numbers

2+1+0=3

3+2+1=6

6+3+2=11

11+6+3=20

20+11+6=37

37+20+11=68

?=68

i think ur doing a version of the Fibonacci number which is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

it is x + # before it

so 0+1=1 1+1=2 2+1=3 ...

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• 3 weeks later...

* 8723, 3872, 2387, ?

?=7238 (the numbers rotate positions one place to the right)

* 1, 4, 9, 18, 35, ?

?=? even the solution didn't make any sense, not sure what x represents

* 23, 45, 89, 177, ?

?=353 (double then subtract 1)

* 7, 5, 8, 4, 9, 3, ?

* 11, 19, 14, 22, 17, 25, ?

* 3, 8, 15, 24, 35, ?

?=48 (add the odd number 5, add the next odd number:7, add the next odd number:9 etc.)

* 2, 4, 5, 10, 12, 24, 27, ?

?=54 (multiply by 2, add 1, multiply by 2, add 2, multiply by 2, add 3, multiply by 2)

* 1, 3, 4, 7, 11, 18, ?

?=29 (add the previous two numbers together (with the exception of going from 1 to three where there is no previous number)

* 99, 92, 86, 81, 77, ?

?=74 (subtract 7, subtract 6, subtract 5, subtract 4, subtract 3)

* 0, 4, 2, 6, 4, 8, ?

* 1, 2, 2, 4, 8, 11, 33, ?

?= sn00bino handled this one quite nicely

... and with that, I'm going to bed. I'll catch up on the rest later.

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call me a nerd, I had to do one more

* 1, 2, 6, 24, 120, ?

?=720 (multiply the number by 1 then add it to itself, multiply the number by 2 then add it to itself, multiply the number by 3 then add it to itself, multiply the number by 4 then add it to itself, multiply the number by 5 then add it to itself)

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• 2 weeks later...

1,4,9,18,35,.....68

this was a reply I wrote down but cant remember how i got it, I jotted down 35+33=68 off to the side but I cant figure why.....hmmmm oh i got it 1 (2 spaces) 4 (4 spaces) 9 (8 spaces) 18 (16 spaces) 35 (32 spaces) 68 (64 spaces) 133 etc. etc.

23,45,89,177,.....303 23(+22) 45 (+44) 89(+88) 177(+176) 303(+352) 655 etc. etc.

I guess this proves there is more than one possible answer

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#02= (1, 4, 9, 18, 35,) 68, 133 (double previous solution quantity minus one: 3, 5, 9, 17, 33, 65)

#18= 2,3,2,3,2,4,2,3,2,3,2,5 (repetitive sequence)

sn00bino, you have 8*3=33 and 33+4=47 for #11? i think you meant:

8+3=11

11*3=33

33+4=37

37*4=148

Here's one for ya:

26, 25, 52, 50, 5, 4, 40, 39...?

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* 1, 4, 9, 18, 35, ?

1*2+2=4

4*2+1=9

9*2+0=18

18*2+(-1)=35

35*2+(-2)=68

68*2+(-3)=133

133*2+(-4)=162

etc.

So you multiply by two and then add one less number each time starting by adding 2.

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an interesting number sequence AHEM CUBA :

26,25,52,50,5,4,40,39... the next is 93 , but does 91 follow ?

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• 5 weeks later...

For the 1,2,3,6,11,20,37,68 ... Someone didn't know the relationship between 1 and 2 ... recall this, it is a recursive equation which involves the three previous numbers, therefore the first three numbers are just given with no relationships between them!

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• 1 month later...

* 8723, 3872, 2387, 7238

* 1, 4, 9, 18, 35, 68

* 23, 45, 89, 177, 353

* 7, 5, 8, 4, 9, 3, 10

* 11, 19, 14, 22, 17, 25, 20

* 3, 8, 15, 24, 35, 48

* 2, 4, 5, 10, 12, 24, 27, 54

* 1, 3, 4, 7, 11, 18, 29

* 99, 92, 86, 81, 77, 74

* 0, 4, 2, 6, 4, 8, 6

* 1, 2, 2, 4, 8, 11, 33, 37

* 1, 2, 6, 24, 120, 720

* 1, 2, 3, 6, 11, 20, 37, 68

* 5, 7, 12, 19, 31, 50, 81

* 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322

* 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, 485

* 4, 7, 15, 29, 59, 117, 235

* 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 5, 2

* 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, 4

This is the kind of thing I trained my math skills with as a kid. Nice flashback

BoilingOil

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• 1, 2, 2, 4, 8, 11, 33, ?

1 + 1 = 2

2 * 1 = 2

2 + 2 = 4

4 * 2 = 8

8 + 3 = 11

8 * 3 = 33

33 + 4 = 47

47 * 4 = 188

...

8 * 3 = 33 ????

33 + 4 = 47 ????

My memory might be failing me, because my basic math classes were over 40 years ago. Or maybe someone discovered new relationship between numbers. But I don't think so

Of course you meant: 11 * 3 = 33, 33 + 4 = 37

and the last line would then be 37 * 4 = 148

At least, if the old maths I learned are still valid

BoilingOil

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1,4,9,18,35,.....68

this was a reply I wrote down but cant remember how i got it, I jotted down 35+33=68 off to the side but I cant figure why.....hmmmm oh i got it 1 (2 spaces) 4 (4 spaces) 9 (8 spaces) 18 (16 spaces) 35 (32 spaces) 68 (64 spaces) 133 etc. etc.

23,45,89,177,.....303 23(+22) 45 (+44) 89(+88) 177(+176) 303(+352) 655 etc. etc.

I guess this proves there is more than one possible answer

177(+176) = 303 ????

Try that again, please. It should be 353

Ofcourse, the next one will then be wrong as well. It should read 353(+352) = 705

BoilingOil

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• 2 weeks later...
*

This is the kind of thing I trained my math skills with as a kid. Nice flashback

BoilingOil

yeah we r still doin this kinda thing now

i think they should put som harder ones on cos face it , im 12 an i can do all of these

so how easy must u guys find iit!!!!!!

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• 4 weeks later...

1,2,3,6,11,20,37...68

a+b+c=d,b+c+d=e,c+d+e=f...

...I think?

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• 3 weeks later...

This is more satisfactory to me as a mathematical operation versus just rotating number order physically

Given 8723

subtract 4851

Given 3872

subtract 1485

Given 2387

Observing 4851 then 1485, the next subtraction number would be 5148

subtract 5148

ans: -3239

Yog

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• 1, 2, 2, 4, 8, 11, 33, ?

1 + 1 = 2

2 * 1 = 2

2 + 2 = 4

4 * 2 = 8

8 + 3 = 11

8 * 3 = 33

33 + 4 = 47

47 * 4 = 188

...

8 * 3 = 33 ????

33 + 4 = 47 ????

My memory might be failing me, because my basic math classes were over 40 years ago. Or maybe someone discovered new relationship between numbers. But I don't think so

Of course you meant: 11 * 3 = 33, 33 + 4 = 37

and the last line would then be 37 * 4 = 148

At least, if the old maths I learned are still valid

BoilingOil

According to sn00bino's attempt and BoilingOil correction, the 2nd unlisted # would be 148. However, I don't think that sequence is accurate. The numbers to the right of the = form the sequence, but what about the first number "1"? sn00bino almost has it. The correct sequence involves alternating "+" and "*", but the modifying values are not entirely correct. So, here is my opinion of the solution:

1 * 1 = 1

1 + 1 = 2

2 * 1 = 2

2 + 2 = 4

4 * 2 = 8

8 + 3 = 11

11 * 3 = 33

33 + 4 = 37

37 * 5 = 185

Here, we have alternating formulas (please think of the non-bold (n)'s and (n+1) as subscript counters instead of coefficients because I don't have actual subscript to work with):

a(n) * b(n) = c(n)

c(n) + n = a(n+1)

Every b(n) = Fibonacci(n). (ie 1,1,2,3,5,8...)

I should note that n does NOT represent a location in the sequence of single digits, but instead represents a location of paired digits:

For {1,2}, n = 1

For {2,4}, n = 2

For {8,11}, n = 3

For {33,37}, n = 4

For {185,190}, n = 5

And so on...

Of course, I think that sn00bino's and BoilingOil's observation were impressive nonetheless. Also, you could argue that their sequence is still correct by saying that the first digit "1" is just a starting point and the formula's do not start until the second digit.

Please correct me if I'm wrong, made a typo, and just plain don't agree.

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• 2 weeks later...
• 1, 2, 2, 4, 8, 11, 33, ?

1 + 1 = 2

2 * 1 = 2

2 + 2 = 4

4 * 2 = 8

8 + 3 = 11

8 * 3 = 33

33 + 4 = 47

47 * 4 = 188

...

Nicely done, though as someone already pointed out, 33 + 4 = 37, not 47, and 37 * 4 = 148, not 188. But nice job cracking it.

Another possibility: Include the inferred zero on the front, and you have, taking the numbers in successive (interlocking) pairs:

Start out with {0, 1}

+1 + (0 + 1) = 2 : (2 - 1) * 2 = 2 -- now we have {0, 1, 2, 2}

+0 + (2 + 2) = 4 : (4 - 2) * 4 = 8 -- now we have {0, 1, 2, 2, 4, 8}

-1 + (4 + = 11 : (11 - * 11 = 33 -- now we have {0, 1, 2, 2, 4, 8, 11, 33}

-2 + (11 + 33) = 42 : (42 - 33) * 42 = 378 -- now we have {0, 1, 2, 2, 4, 8, 11, 33, 42, 378}

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• 1 month later...
i think ur doing a version of the Fibonacci number which is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

it is x + # before it

so 0+1=1 1+1=2 2+1=3 ...

try 0/1 1/1 2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 89/55 ......

What number do the quotients swing around?

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• 1 month later...

2. 1,4,9,18,35,68

2x+2,1,0

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• 3 weeks later...

1, 4, 9, 18, 35, ?64

1+3=4

4+5=9

7

9+9=18

11

13

15

18+17=35

19

21

23

25

27

35+29=64

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126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ?479

126+63+1=190

------------------286-190=96

--------------------------------144-96=48

--------------------------------------------72-48=24

190+95+1=286

------------------430-286=144

---------------------------------216-144=72

-----------------------------------------------108-72=36

286+143+1=430

------------------646-430=216

---------------------------------324-216=108

------------------------------------------------156-108=48

430+215+1=646

------------------970-646=324

---------------------------------480-324=156

646+323+1=970

------------------1450-970=480

970+479+1=1450

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1, 2, 3, 6, 11, 20, 37, ?46

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