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## Whatever Next?

Posted by trickofmind on June 6, 2010 – 1:09 am

What is the next number in the sequence:

32 – 35 – 40 – 44 – 52 – 112 – ?

- Karl Sharman

This post is under “SharedPuzzle” and has 35 respond so far.

### 35 Responds so far- Add one»

1. 1. TheWyvern Said：

112 ,124 ,144 ,192 ,432 ???

2. 2. Karl Sharman Said：

TheWyvern…. Nope.
PS, Nothing to do with the question/answer, do you read Stephen Erikson – hence the name TheWyvern?

3. 3. TheWyvern Said：

no i have not seen anything like this before !,but i actually know what is the meaning of my nickname -wyvern-!. ps, i am in a secondary school so i am just interesed in study now :b not reading ,my exams after fortnight ,but you can add my e-mail. o.spiderhack@yahoo.com , just for more knowledge :d

4. 4. Random Guy Said：

Is it “What”? If it is, What is not a number.

5. 5. cheater Said：

146

6. 6. Euclid's Brother Said：

140, 176, 228?, 582?

7. 7. Mohamed Said：

32, 35, 40, 44, 52, 112
3, 5, 4, 8, 60
2, -1, 4, 52
3, 5, 48
8, 43
35

This is weird! Seems this sequence is not even arithmetic, right?

8. 8. Emily N. Said：

Hi, I’m very interested in Linux but Im a Super Newbie and I’m having trouble deciding on the right distribution for me (Havent you heard this a million times?) anyway here is my problem, I need a distribution that can switch between reading and writing in English and Japanese (Japanese Language Support) with out restarting the operating system.

9. 9. Anonymous Said：

Looks like folks are struggling….

All the numbers are 32 in decending bases starting at base 10
32=3*10+2*1=32
35=3*9+5*1=32
40=4*8+0*1=32
44=4*7+4*1=32
52=5*6+2*1=32
112=1*25+1*5+2*1=32
next number is
200 in base 4 =2*16+0*4+0*1=32

Cam

10. 10. Euclid's Brother Said：

Nice puzzle.. don’t tell my brother I didn’t figure it out.. I’ll never hear the end of it..

11. 11. TheWyvern Said：

Mohamed i was thinking about these numbers,but i found that there nothing attach them together!!

12. 12. Vago Said：

I dont have enough time to solve it completely. so ill just put what I would do to solve it, note: this is a verrrry long process.
32 – 35 – 40 – 44 – 52 – 112 –
Take a polnomial of the 6th degree
p(x) = Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex + F
now form 6 equations like this:
p(1) = 32
p(2) = 35
p(3) = 40
p(4) = 44
p(5) = 52
p(6) = 112

Hence after finding all the constants, A,B,C,D,E,F, we should input x value as 7 an hence the next number is formed.

Now u see why i didnt want to solve it completely

13. 13. Mohamed Said：

Looks like Cam got it right. How did you spot that Cam?

14. 14. Anonymous Said：

Mohamed,

Basically the process that I went by was as follows:

Eliminate the obvious:
-Series is not arithmatic (should be first check for most series)
-Series does not appear to be letter substitution (gap between largest and smallest number is >26)

Look for hints as to what it might be:
-No digit great than 5 is used (suggesting number base may be restricting largest value of digits)
-nearly linear then nearly exponential increase (suggesting decreasing number bases may be used)
-the number with the largest number of digits has small values for the individual digits (highly suggestive that the
largest number is using a smaller number base)

Had the number 112 not been included in the series then the series would have been a lot more difficult to figure out as it would have eliminated 2/3 of the hints I mentioned.

That’s what my thought process was anyhow.

Cam

15. 15. Mohamed Said：

Nice Cam. Well done!

16. 16. Chris Said：

Hi Cam. Nice to see you back.

17. 17. Karys Said：

Continuing on Vago’s idea…
Thanks to Open office Calc,

A=0,2916666…=875/3000

B=-4,04166667=12125/3000

C=20,95833333=62875/3000

D=-49,95833333=149875/3000

E=57,75000000=57.75

F=7,00000000=7

P(7)=350.

(too lazy to simplificate…)

18. 18. Karys Said：

Hey, dunno if it is O.Office losing precision, but we have
p(8)=1004,999…890000… about 1005, maybe the intermediate calculations aren’t precise enough to have an integer, maybe it is not actually 1005…
p(9)=2463,9999..62= 2463 approximately
p(10)=5297 approx

until p(100)= 2532964531,99913000000000000000 a little less nines.

19. 19. Karl Sharman Said：

Cam is first in with the correct answer.

Karl

20. 20. Gary Holmes Said：

1) Cam must be a genius…! IQ must be 200…?

She (he) mentioned “decending bases” of 10 all the way down to 5 and 4. I followed those.

But, where did the “1*25″ come from, pls?

Also, where did the “2*16″ come from, pls?

“”
All the numbers are 32 in decending bases starting at base 10
32=3*10+2*1=32
35=3*9+5*1=32
40=4*8+0*1=32
44=4*7+4*1=32
52=5*6+2*1=32
112=1*25+1*5+2*1=32
next number is
200 in base 4 =2*16+0*4+0*1=32

Cam
“”

2) Karl S said, 200 is correct.

Then, the next number should be in base 3:
a*x + b*3 + c*1 = 32
2*15 + 0*3 + 2*1 = 30 + 0 + 2 = 32.
202

Cam and Karl,
Is 202 the correct next number, pls?

3) Assuming 202 is correct,
then the further next one has to be Base 2:
a*x + b*2 + c*1 = 32
2*15 + 1*2 + 0*1 = 30 + 2 + 0 = 32.
A: 210

4) Assuming 210 is correct,
then the further next one has to be Base 1:
a*x + b*1 + c*1 = 32
2*15 + 1*1 + 1*1 = 30 + 1 + 1 = 32.
A: 211

4) Folks, pls be patient? This 1 has 2b the last. Assuming 211 is correct,
then “the Last but not the Least” has to be Base 0:
a*x + b*0 + c*1 = 32
2*15 + 1*0 + 2*1 = 30 + 0 + 2 = 32.
A: 212

“ELEMENTARY…”

5) Ps, I still have problem re “1*25″; “2*16″; and “2*15″. They do not sound logical. Instead, sound like miscarriage (Pulling out forcefully…, to fit the needs…)

Gary Holmes

21. 21. Chris Said：

The next number (i.e. in base 3) is:
1*27 + 0*9 + 1*3 + 2*1, i.e. 1012
and the next number (i.e. in base 2) is:
1*32 + 0*16 + 0*8 + 0*4 +0*2 + 0*1 = 100000

The logical continuation to base 1 is:
11111111111111111111111111111111 (that’s 32 1s).

There is no sensible way to define base 0 that I’m aware of.

22. 22. Chris Said：

Hi Gary. The “digits” go up in powers of the base.
So base 5 goes: 1s, 5s, 25s, 125s, 625s

23. 23. Karys Said：

Gary, let me explain how bases work.

First of all, nowadays we often count in base 10.

It uses 10 digits, 0 1 2 3 4 5 6 7 8 9
If you want to write 9+1, that is a number greater than the greatest digit, you have to write 10, that is 10= 1*10^1 +0 (FYI x^n, x power/exponent n means x*x*x…*x n times)

One hundred is 10^2, and 21459 is 2*10^4 + 1*10^3 + 4*10^2 + 5*10 + 9
etc.
The position of the digit gives the power of the base to which the digit is multiplied.

It’s the same with other bases. Another mostly used with computers is base 2 (commonly called binary): you write with 0s and 1s, 35 in base 10 gives :
35(base10) = 1*2^5 + 0*2^4 + 0*2^3 + 0*2^2 + 1*2 + 1 = 100011 (base2)
Note that 10 is 2 in base 2.

(“There are only 10 types of people in the world: Those who understand binary, and those who don’t”)

So when Cam writes 112=1*25+1*5+2*1=32, 112(base5) = (1)*5^2 + (1)*5^1 + (2)*5^0 = 32(base10)

you also have bases greater than 10, essentially 16, above 9, we have 6 other digits, commonly written A=10 B=11 C=12 D=13 E F.

so ABC(base16)=A*16^2 + B*16^1 + C*16^0 = 10*16^2 + 11*16^1 + 12*16^0

The fact that we usually have base 10 numbers is because of our fingers (or so it is said). Ppl say time is commonly measured with base 60, you have 60 units (seconds) in one minute, 60 minutes in one hour.

So if I say you posted your message at 11:10′35”, the number we are talking about is :
(11)(10)(35) (base60) = 11*60^2+10*60+35 = a lot of seconds.

Personaly I think it’s a shame people don’t count in base 2… Imagine, in a rocket launching…
Rocket launching in one thousand and ten… one thousand and one… one thousand… one hundred and eleven… one hundred and ten… one hundred and one… one hundred… eleven… ten…one…ZERO.
fun.

Base 2 is practical, since to a machine it is easier to tell it “yes” (1) and no (0), with “current”, “no current”, than “blue”,”light blue”, “dark blue”, “cyan”… That’s what some people don’t understand when they have problems with their computer… they believe it’s like magic and ABRACADABRA you input something it outputs something accordingly. No, just “yes”s and “no”s, and a loooooooooooong sequance of these will get you a number, and a lot of numbers mean a lot of information, a lot of options etc…

Continuing on the subject.
Hopefully you have understood my little lesson above ^^

To have a number from base n to base 10, you just write it as shown above, and just usual calculus (that is, in base 10, duh… I suppose since you didn’t know much about bases, you don’t “usually” do calculus in base 16…)

To have a number from base 10 to base n, you have to write it in a sum of a*n^k, a<n, k an integer.
One method is to use euclidean division.(if you do not know about it, I invite you to go on the wikipedia article…or whatever that could teach you)

Next step we want 32(base10) in base 3. In base 10 we do the euclidean division of 32 by 3 :
32=3*10+2

The remainder 2 will be the last digit of the base 3 32. Take the quotient and divide it again :
10=3*3+1

1 shall be the penultimate digit (just showing off…)

Take the last quotient etc until you get a quotient smaller than 3 (or the base you want to convert into…)

So : 32=1*3^3+0*3^2+1*3+2 = 1012(base3)

32(base10)=10000(base2)
(I think the windows calculator can convert between base 2 , 10 and 16)

AND finally 32(base10)=111111111111111111111111111111111(base1)

Yeah, that's the most basic way of counting, and that was the first one (best for additions and multiplications, but it shall take a little longer time having all the 1s drawn -the shape of the digit is of no importance, you may notice it is all arbitrarily chosen- than multiplying having learnt the tables…)

Base 0 is unusable.

I heard of rational bases, such as base pi… writing
(a)(b)(c)=a*pi^2 + b*pi + c…

24. 24. Chris Said：

http://en.wikipedia.org/wiki/Numeral_system

25. 25. Anonymous Said：

Gary Holmes,

Quick lesson in number bases:

In any number base system:
The 1st digit to the left of the decimal is the base to the power of 0 (i.e. 1)
The 2nd digit to the left of the decimal is the base to the power of 1
The 3rd digit to the left of the decimal is the base to the power of 2
The 4th digit to the left of the decimal is the base to the power of 3…..etc.

e.g.
the standard base 10 system we use

981 is
1*10^0=1*1=1
8*10^1=8*10=80
9*10^2=9*100=900

1+80+900=981

Note that the digit first left of the decmal is the 1s place, the 2nd is the 10s, the 3rd is the 100s

now for 112 in base 5
2*5^0=2*1=2
1*5^1=1*5=5
1*5^2=1*25=25

2+5+25=32

Note that the digit first left of the decmal is the 1s place, the 2nd is the 5s, the 3rd is the 25s

As far as the question as to what the remaining numbers in the series would be:
32 must be converted base 4, then base 3, then base 2, then base 1

I have added 32 to base 5 conversion as an additional example.
32 in base 5
25< 32 <125
32/25= 1R7
7/5=1R2
2/1=2R0

32=112 in base 5

32 in base 4
16<32<64
32/16=2R0
0/4=0R0
0/1=0R0

32=200 in base 4

32 in base 3
27<32<81
32/27=1R5
5/9=0R5
5/3=1R2
2/1=2R0
32= 1012 in base 3

32 in base 2
32=32=32
32/32=1R0
0/16=0R0
0/8=0R0
0/4=0R0
0/2=0R0
0/1=0R0
32=100000 in base 2

32 in base 1
1 to the power of anything is still 1. So 32 in base 1 is a string of 32 1s.
32= 11111111111111111111111111111111 in base 1

base 1 is the end of the road as 0 to the power of anything is still 0 thus a non-zero quantity can not be represented in a base zero system.

So the series taken to its terminating point would be:
32, 35, 40, 44, 52, 112, 200, 1012, 100000, 11111111111111111111111111111111

Hopefully that clarifies things.

Cam

26. 26. Chris Said：

Ooops, I didn’t mean to post the previous comment. See http://en.wikipedia.org/wiki/Numeral_system for an explanation of positional number systems.

27. 27. Chris Said：

LOL. Looks like a lot of posts appeared almost together. What a helpful lot we seem to be.

28. 28. Karl Sharman Said：

The best explanation for base systems goes to……

…….Karys… Yaaaayyyyy! The crowd goes wild.

Cam comes in as the runner up only because he posted half an hour after Karys, but a great explanation nonetheless.

29. 29. Karys Said：

lol ^^
thanks Never thought that some day I would be the best explainer at something… thanks to ToM ^^

30. 30. Gary Holmes Said：

To:
Cam; Vago; Chris; & Karys;

U guys (gals) must b a bunch of Mathematicians, Computer Gurus, & Rocket Scientists.

Thank u 4 ur educations.

Ur pointers brought up a New topic — Anybody cares to comment, pls:

We, Earthmen, use Base-10 (since we’ve 10 fingers):
* Ten is 10.
* Hundred is 10*10 = 100.
* Thousand is 10*10*10 = 1000.

Roswell Aliens use Base-12 (since they’ve 12 fingers):
* Ten is 12.
* Hundred is 12*12 = 144.
* Thousand is 12*12*12 = 1728.
* Presumably, their Ten, Eleven, & Twelve would be T, V, & W.
* Hence, their Twelve would be 1X or 10 or 1W?

Was told: Their system is more advanced & effective.

Why so? What r the advantages? What r the impacts of their nemeric system on everything else in their “world”?
(Needless to say, their computers would function differently than ours also?)

Would their Hundred-Dollar Bill show \$100? Or \$1XX? Or \$1WW? Or \$144?
(Needless to say, their Quarters would be 36 Pennies.)

31. 31. Karl Sharman Said：

Mesopotamians used base 12, based on the 12 joints on the 4 fingers of a hand. The other hand, with five fingers gave them the ability to work up to 60.

This lead to the 60 seconds/minutes and hours and 12 segments of 5 minutes to the hour.

Aliens have been here before it would seem.

Karl

32. 32. Karys Said：

Base 12, twelve is 10(base12). No need of a W=12 in base 12, like there is no T in base 10 if that’s what you asked.

BTW, I’m not mathematician, maybe I’d like to be one someday, but I have not finished my studies yet… xD

33. 33. Chris Said：

You do need T, V, W to write what we write in decimal as 10, 11 and 12. – they would be written as T, V and W respectively.

The hexadecimal system use A, B, C ,D and E to represent 10 – 15.

The reason that people sometimes propose base 12 is because it’s divisible by 2,3,4,6 and 12 and somehow think this will make division easy. You have just as much work to do to calculate 12345/678 whatever base you choose.

However, due to obvious technical difficulties, base 2 is used by most computers to perform calculations. Base 2 only requires 0 and 1 to represent numbers.

34. 34. Chris Said：

Ooops again. Too tired last night, Karys is right, no W for 12.