A Difficult Math

[WaiWai]

Originally posted by: Savarak

Originally posted by: WaiWai
A Difficult Math

12 (21) 26

16 (30) 36

20 (38) 48

24 (54) 60

28 ( ? ) 84

Each numeral series stands on its own.
Ther relationship is among the first/second/third numbers.
The relationship is the same for each numeral series.
But each numeral series does not affect each other.

I figured it out... the answer is "28 ( [any number greater than 37 and less than 79] ) 84"

it fits...
1. series still stands as its own..
2. relationship is that the middle number is at least 9 greater than left number, and at most 5 less than right number
3. relationship as mentioned in 2. is the same for each
4. each series stands does not affect the others

Think outside the box here! 😉

😀 How creative you are!
Hopefully your answer will be correct.

 

[Savarak]

bump for a real answer

 

[DrPizza]

Let me refer you to the "Online Encyclopedia of Integer Sequences"
here

Unfortunately, sequence 2 and 3 aren't found (there are over 100,000 different sequences indexed there... those two must be really really obscure if they're not listed on the OEIS site. Try to think of your own sequence based on some rule... put it in the search engine on that site, and it'll probably find your sequence. (heck, sometimes I've put in the first 5 integers and have been greeted with quite a few sequences that work.)

 

[DrPizza]

As I look at the second and third sequences.. perfect squares, and primes keep popping out at me.

Hmmm... on a whim, I subtracted 4 from each term in the middle sequence... suddenly stuff popped up at OEIS.
Going with OEIS's sequences, I'd guess the parentheses can be filled in with: 65

Look at the second sequence in this link:
here

 

[JDrake]

Originally posted by: DrPizza
Let me refer you to the "Online Encyclopedia of Integer Sequences"
here

Unfortunately, sequence 2 and 3 aren't found (there are over 100,000 different sequences indexed there... those two must be really really obscure if they're not listed on the OEIS site. Try to think of your own sequence based on some rule... put it in the search engine on that site, and it'll probably find your sequence. (heck, sometimes I've put in the first 5 integers and have been greeted with quite a few sequences that work.)

Woah I never knew of that site
bookmarked it

 

[musicman87]

?=rand()%72+12;

 

[Savarak]

Originally posted by: DrPizza
As I look at the second and third sequences.. perfect squares, and primes keep popping out at me.

Hmmm... on a whim, I subtracted 4 from each term in the middle sequence... suddenly stuff popped up at OEIS.
Going with OEIS's sequences, I'd guess the parentheses can be filled in with: 65

Look at the second sequence in this link:
here

I dont think that works...
the first one shows up 12 (21-4 = 17) 26
the second one doesn't show up 16 (30-4 = 26) 36
the third one doesn't show up 20 (38-4 = 34) 48
etc...

besides... the middle numbers aren't reliant on the other numbered series, they are reliant on the first and third numbers of their respective series

 

[Kelemvor]

So what's the answer to this thing?

 

[Kyteland]

You are given 4 sequences to work with. If you set up any (solvable) 4 variable system of equations you will get an answer for this.

For example, if you label your 3 columns A, B and C you can do:
A*w + C*x + A*C*y + A*B*z = B*C

Which sets up the system:
12*w + 26*x + 312*y + 252*z = 546
16*w + 36*x + 576*y + 480*z = 1080
20*w + 48*x + 960*y + 760*z = 1824
24*w + 60*x + 1440*y + 1296*z = 3240

Which solves to:
w = -6858/26
x = 3468/26
y = -50/26
z = 87/26

When you solve for B you get:
B = (3468*C - 6858*A - 50*A*C)/(26*C - 87*A)

That makes the 5th column solve to 218/3. That is only one of many possible answers.

 

[Vich]

this thread doesnt make any sense. I only went up to pre-calc, lol. :Q

 

[Kyteland]

Originally posted by: Vich
this thread doesnt make any sense. I only went up to pre-calc, lol. :Q

Well since you only need basic algebra to do it, you should feel right at home. 😉

 

[IHateMyJob2004]

Originally posted by: StrangerGuy

Originally posted by: WaiWai

Originally posted by: tfinch2
42

Why?
You have to explain why.

It's the answer to everything. Duh.

The ultimate answer it is.

 

[Vich]

Originally posted by: Kyteland

Originally posted by: Vich
this thread doesnt make any sense. I only went up to pre-calc, lol. :Q

Well since you only need basic algebra to do it, you should feel right at home. 😉

:frown:🙁

 

[Kyteland]

So did I get it right OP?

 

[Vich]

Define the function f(x,y) on pairs of integers by:
f(12,26) : = 21
f(16,36) : = 30
f(20,48) : = 38
f(24,60) : = 54
f(28,84) : = 23 * 42
and
f(x,y) : = \frac{\zeta(x^2+y^2+\Gamma(\frac{1}{\gamma})) - \sigma(xy) }{\vartheta(e \cdot x+i\cdot(y^4+\pi))}
otherwise.

So the number you are looking for is 23 * 42 = 966

If u cant understand the equation above here it is in picture format.
Text

There is your answer!

 

[Vich]

right or wrong?

 

[crystal]

65.

 

[Vich]

Originally posted by: crystal
65.

Dont think so

 

[WaiWai]

Originally posted by: Vich
Define the function f(x,y) on pairs of integers by:
f(12,26) : = 21
f(16,36) : = 30
f(20,48) : = 38
f(24,60) : = 54
f(28,84) : = 23 * 42
and
f(x,y) : = \frac{\zeta(x^2+y^2+\Gamma(\frac{1}{\gamma})) - \sigma(xy) }{\vartheta(e \cdot x+i\cdot(y^4+\pi))}
otherwise.

So the number you are looking for is 23 * 42 = 966

If u cant understand the equation above here it is in picture format.
Text

There is your answer!

Sorry, it's wrong!

The last pair should be:
f(28, ?) = 84
but NOT f(28, 84) = ?

 

[WaiWai]

Here's my thought!
Calculate the middle value between the first and third number, * compare it with the middle one.
Can you see something in common?

 

[WaiWai]

Originally posted by: Injury
What if OP got the numbers wrong on the fourth one. 😉

I wish I had! 🙁

 

[sao123]

so you as the OP dont really have the answer?????


wtf is going on here.

 

[ashakar]

What class is this problem for? or where did you get the problem from.

 

[DaShen]

Originally posted by: WaiWai

Originally posted by: Vich
Define the function f(x,y) on pairs of integers by:
f(12,26) : = 21
f(16,36) : = 30
f(20,48) : = 38
f(24,60) : = 54
f(28,84) : = 23 * 42
and
f(x,y) : = \frac{\zeta(x^2+y^2+\Gamma(\frac{1}{\gamma})) - \sigma(xy) }{\vartheta(e \cdot x+i\cdot(y^4+\pi))}
otherwise.

So the number you are looking for is 23 * 42 = 966

If u cant understand the equation above here it is in picture format.
Text

There is your answer!

Sorry, it's wrong!

The last pair should be:
f(28, ?) = 84
but NOT f(28, 84) = ?

If you follow Vich's proof, it is f(28,84) = ?

I don't know if that is the answer though, but it is possible.

 

[randumb]

Originally posted by: Vich
Define the function f(x,y) on pairs of integers by:
f(12,26) : = 21
f(16,36) : = 30
f(20,48) : = 38
f(24,60) : = 54
f(28,84) : = 23 * 42
and
f(x,y) : = \frac{\zeta(x^2+y^2+\Gamma(\frac{1}{\gamma})) - \sigma(xy) }{\vartheta(e \cdot x+i\cdot(y^4+\pi))}
otherwise.

So the number you are looking for is 23 * 42 = 966

If u cant understand the equation above here it is in picture format.
Text

There is your answer!

:laugh: