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More ways to get Braingle...

Formula

Math brain teasers require computations to solve.

 

Puzzle ID:#20276
Fun:** (1.83)
Difficulty:**** (3.35)
Category:Math
Submitted By:DakarMorad**
Corrected By:lessthanjake789

 

 

 



If you use a certain formula on 13, you end up with 7.

Under the same formula, 2352 becomes 16, 246 becomes 14, 700 turns into 16, and 1030 becomes 14.

What would 9304 become?

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Comments

I_am_the_Omega**
Jan 08, 2005

Doesn't 9304 convert to 00111001 00110011 00110000 00110100? ...
chimpe81
Jan 09, 2005

To Easy
DakarMorad*
Jan 09, 2005

Omega: 9304 is 8192 + 1024 + 64 + 16 + 8.

Orange: Well, your a first. ;)

Sorry that this teaser was so difficult. It's my first.
saucyangel**
Jan 10, 2005

ok, i NEVER would have figured that out! (well, maybe after i sat there and thought about it for an hour or three...) good one!
cloud_strife**
Jan 18, 2005

err... what is a binary??
AtropusAnz*
Jan 18, 2005

Odd.. I guessed it had to do with binary.. but it was really just too obscure.
For your next one perhaps you chould add a hint ^_^
God-sGrace2005*
Jan 23, 2005

I don\'t get it and what is binary?
DakarMorad*
Jan 24, 2005

Atropus: I\'ll keep that in mind.

Binary is a system of counting that uses only 1s and 0s instead of 1-9 as digits.

1 is one,
10 is two,
11 is three,
100 is four,
etc.
CPlusPlusMan*us*
Jan 30, 2005

I wouldn't necessarily call a binary conversion a formula, but great teaser anyways! When I saw it wasn't a function, it had me really thrown off. I'd never of even guessed of binary!
Gandalf**
Feb 14, 2005

it was hard but when my sister got it i felt so embarresed evn though shes older then me
sftbaltwty*us*
Feb 17, 2005

haha..i always knew there was reason i stopped taking math and stuck to english........
waffle*
Feb 27, 2005

How were we ever supposed to arive at that answer?
ben2Akr*
Apr 07, 2005

great one
(user deleted)
Apr 23, 2005

i got -24345

a 6th order polynomial will pass through all those points.

eq looks something like this:

f(x) = -6.43551381261098E-12*x^4 + 3.63684663115652E-08*x^3 - 0.0000674643206344868*x^2 + 0.0452940004077013*x + 6.42249974693123

but yeah adding the digits in a bianary representation will give you something else
(user deleted)
Apr 23, 2005

sorry that's the 4th order regression eq
sweetime**
May 16, 2005

i know what binary is, but have never used it in my whole life.
how does 10010001011000 = 19?
darthforman*
May 22, 2005

solidtanker*
Jun 10, 2005

These kinds of puzzles are not my favorite because anyone can come up with an arbitrary system to convert one number into another. There are infinite ways to do so.
rashadAma*
Jun 11, 2005

I feel so jealous because some of you understood it and I didn't get a single atom of it!!!
schatzy228*us*
Aug 27, 2005

great teaser,,those who didnt like it just dont get the concept of "teaser",,,,but its all good
soccercow10Aus*
Aug 29, 2005

HuH!?!?!?
that was a fun teaser to try and find out !!
even though i didnt
all i have to say is creative.....creative indeed
i_am_hatedAus*
Sep 28, 2005


!!!
usaswimAus*
Oct 28, 2005

mrbrainyboy*us*
Nov 18, 2005


The hardest teaser in the whole site...
wow
lovefrenzy**
Nov 30, 2005

what
qqqq*
Dec 20, 2005

My head hurts.
teen_wizAca*
Feb 09, 2006

Ow. My brain is killing me.
coolblue*um*
May 21, 2006

So many zeroes, and who the heck heard of the binary system?
sftball_rocks13*
Jun 14, 2006

huh.......
soccercow10Aus*
Nov 20, 2006

can someone please explain this to me? lol sorry too hard
(user deleted)
Feb 02, 2007

To all who dont get it:

If you dont know binary you're screwed before you even started. Look up "binary" in wikipedia if you dont even know what it is.

A summary: Computers use binary to represent data, since computers work with circuits that have two states, off (0) and on (1). A computer can represent numbers, strings, or you're favourite MP3 as a string of 0's and 1's. Now that thats out of the way...

With his conversion system, a table of values goes like this:
0,1,10,11,100,101,110,111,1000,1001,1010
Number = Binary = Value*
0 = 0 = 1
1 = 1 = 2
2 = 10 = 3
3 = 11 = 4
4 = 100 = 4
5 = 101 = 5
6 = 110 = 5
7 = 111 = 6
8 = 1000 = 5
9 = 1001 = 6
10 = 1010 = 6
11 = 1011 = 7
12 = 1100 = 6
13 = 1101 = 7
14 = 1110 = 7
15 = 1111 = 8

*given that you add 1 for every zero and 2 for every one.

and so on. I actually never new how to convert binary, but I now do just by looking at the conversions.
Good very hard teaser
sftball_rocks13*
Feb 27, 2007

Um... My brain hurts but this was pretty good, I learned binary in school this year, but I would have NEVER gotten that good teaser!
MrDoug
Mar 18, 2007

I don't like this one because it doesn't have a clear (single) correct answer. There are lots of formulas that give the given numbers. For example, one can construct (as already stated) a 4th-degree polynomial which takes on all the valued specified (or infinitely many polynomials of degree 5 or higher), and any of these qualify as a "formula."

It might help to give some clue as to what you had in mind, such as "The formula I have in mind only applies to integers, and it always gives an integer value." This at least rules out continuous mathematics and identifies it as a discrete problem, which is apparently what you intended.
brainglewashed*
Jun 14, 2007

DANG I SAID 1,000,000,000
PojuerAph*
Jun 28, 2007

too hard
Brainyday*us*
Nov 11, 2007

I am confused.
UlsterCharlotteAus*
Jan 14, 2008

I agree with MrDoug. This is WAY too obscure. You realize right away that there are multiple answers. Not good at all. Who proofreads/screens these things anyway?
annvie9*us*
Mar 30, 2008

I would only get this answer if I sat there for a whole day. But if I did, I would staring at the ceiling doing nothing anyways.
(user deleted)
May 07, 2008

As far as I remember, you can't have 14 digits in a binary number - it has to be in sets of 4 (i.e. the number 5 in binary would be 0101, not '101'). So,

9304 becomes 0010 0100 0101 1000, which has 11 zeros and 5 ones, which is 21.
Natrixtca*
May 14, 2008

If you want people to understand this add a hint that says "This number willbe converted into binary."
EvilMonkeySpy3Aus*
Dec 02, 2008

darrhhhhhararrrrrrr...... i'm only in seventh grade.... i had absolutely no idea..... XP
piratechicken92*
Dec 04, 2008

that was waaaaay to hard for me2
javaguru*us*
Dec 10, 2008

Lame. As mentioned before, arbitrarily obscure without a unique or obviously correct answer.

And to greenrazi: You're are probably thinking of hexadecimal (base 16), where each digit can have one of 16 values. A binary representation of a hexadecimal number would have a granularity of 4 bits.
(user deleted)
Apr 10, 2009

Too make things easy to understand i just got the need to post a comment... Here it is(look at CanadaAotS comments)...
14 = 1110
lets convert 1 to 2 and 0 to 1
14 = 2+2+2+1 = 7

15 = 1111
15 = 2+2+2+2 = 8
rashadAma*
May 07, 2009

Wonderful,yet ...impossible.
(user deleted)
Jul 21, 2009

The answer is not A FORMULA.
xandrani
Jan 21, 2010

There is more than one solution. The binary answer is more succinct and sweeter therefore it is the 'official' answer, but this also works:

a = 0.00000000003090981409468774
b = -0.000000087318835992468036
c = 0.000023696152096488413
d = 0.028997981886427873
e = 6.6192125424396062

f(x) = a(x^4) + b(x^3) + c(x^2) + dx + e

So answer would be:
f(9304) = 163621
xandrani
Jan 23, 2010

Note that the above function should strictly have read:

f(x) = floor(a(x^4) + b(x^3) + c(x^2) + dx + e)
Where floor rounds down to the nearest integer.

Note that this can also be written as:
f(x) = ⎣a(x^4) + b(x^3) + c(x^2) + dx + e⎦

See:
http://mathworld.wolfram.com/CeilingFunction.html
xandrani
Jan 23, 2010

I have noticed a few comments stating that the answer is not a function... however aside from the function above I posted (which is one solution), I now also post another function which fits the other solution. Almost anything can be made in to a function.

g(x) = 1 + g(x - 2^⎣logx/log2⎦)
Where x ≠ 0 and g(0) = 0

f(x) = 1 + ⎣logx/log2⎦ + g(x)


Let's try and solve for x = 9304:

f(9304) = 1 + 13 + g(9304)
g(9304) = 1 + g(9304 - 2^13) = 1 + g(1112)
g(1112) = 1 + g(1112 - 2^10) = 1 + g(8
g(8 = 1 + g(88 - 2^6) = 1 + g(24)
g(24) = 1 + g(24 - 2^4) = 1 + g(
g( = 1 + g(8 - 2^3) = 1 + g(0) = 1

So iterating out we get:
9(24) = 1 + 1 = 2
9(8 = 1 + 2 = 3
9(1112) = 1 + 3 = 4
g(9304) = 1 + 4 = 5

So therefore:
f(9304) = 1 + 13 + 5 = 19
xandrani
Jan 23, 2010

The smiley faces with glasses should be '8 )'.
xandrani
Jan 23, 2010

I have noticed a few comments stating that the answer is not a function... however aside from the function above I posted (which is one solution), I now also post another function which fits the other solution. Almost anything can be made in to a function.

g(x) = 1 + g(x - 2^⎣logx/log2⎦)
Where x ≠ 0 and g(0) = 0

f(x) = 1 + ⎣logx/log2⎦ + g(x)


Let's try and solve for x = 9304:

f(9304) = 1 + 13 + g(9304)
g(9304) = 1 + g(9304 - 2^13) = 1 + g(1112)
g(1112) = 1 + g(1112 - 2^10) = 1 + g(8 )
g(8 ) = 1 + g(88 - 2^6) = 1 + g(24)
g(24) = 1 + g(24 - 2^4) = 1 + g(8 )
g(8 ) = 1 + g(8 - 2^3) = 1 + g(0) = 1

So iterating out we get:
9(24) = 1 + 1 = 2
9(8 ) = 1 + 2 = 3
9(1112) = 1 + 3 = 4
g(9304) = 1 + 4 = 5

So therefore:
f(9304) = 1 + 13 + 5 = 19
xandrani
Jan 23, 2010

Damn smilies! I post yet again:

I have noticed a few comments stating that the answer is not a function... however aside from the function above I posted (which is one solution), I now also post another function which fits the other solution. Almost anything can be made in to a function.

g(x) = 1 + g(x - 2^⎣logx/log2⎦)
Where x ≠ 0 and g(0) = 0

f(x) = 1 + ⎣logx/log2⎦ + g(x)


Let's try and solve for x = 9304:

f(9304) = 1 + 13 + g(9304)
g(9304) = 1 + g(9304 - 2^13) = 1 + g(1112)
g(1112) = 1 + g(1112 - 2^10) = 1 + g(88 )
g(88 ) = 1 + g(88 - 2^6) = 1 + g(24)
g(24) = 1 + g(24 - 2^4) = 1 + g(8 )
g(8 ) = 1 + g(8 - 2^3) = 1 + g(0) = 1

So iterating out we get:
9(24) = 1 + 1 = 2
9(88 ) = 1 + 2 = 3
9(1112) = 1 + 3 = 4
g(9304) = 1 + 4 = 5

So therefore:
f(9304) = 1 + 13 + 5 = 19
xandrani
Jan 23, 2010

There are indeed many solutions to this one, here's another just for fun:

n = floor(x / 230)

f(x) = 14 - 7(x mod 2) + (1 - (x mod 2))((n^2 - n) mod 4)

f(9304) = 14
(user deleted)
Apr 13, 2010

Another solution (and perhaps the simplest so far)
f(x) = 16 - ([(x % 14) * 6] % 23)

f(9304) = 14



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