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        riddles >> easy >> Integer inequalities
        
(Message started by: NickH on Nov 30^th, 2004, 2:44pm)

Title: Integer inequalities
Post by NickH on Nov 30^th, 2004, 2:44pm

Find the smallest positive integers A, B, C, D, such that A+A > A+B > A+C > B+B > B+C > A+D > C+C > B+D > C+D > D+D.

(If there is any ambiguity, choose smallest D, then smallest C, then smallest B, and finally smallest A.)

Title: Re: Integer inequalities
Post by towr on Nov 30^th, 2004, 3:43pm

Maybe I'm getting it wrong, but there doesn't seem to be a solution..

Title: Re: Integer inequalities
Post by NickH on Nov 30^th, 2004, 4:38pm

Quote:

Maybe I'm getting it wrong, but there doesn't seem to be a solution..

There is definitely a solution!

Title: Re: Integer inequalities
Post by Aryabhatta on Nov 30^th, 2004, 4:57pm

is it [hide] 1,5,7,10 [/hide]?

Found it easier to work putting B = A-X, C = A-Y and D = A-Z and finding possible values of X,Y,Z.

Title: Re: Integer inequalities
Post by towr on Dec 1^st, 2004, 12:47am

::[hide]0,4,6,9[/hide]::

Title: Re: Integer inequalities
Post by Grimbal on Dec 1^st, 2004, 2:32am

Positive integers!
::[hide]A,B,C,D = 10,7,5,1[/hide]::

Title: Re: Integer inequalities
Post by towr on Dec 1^st, 2004, 7:02am

I'm an optimist, I consider everything that's not negative positive ;)

Title: Re: Integer inequalities
Post by Aryabhatta on Dec 1^st, 2004, 11:27am

on 12/01/04 at 07:02:49, towr wrote:

I'm an optimist, I consider everything that's not negative positive ;)

Wouldn't that make you a realist?
An optimist would consider even a negative as positive.. ;D

Title: Re: Integer inequalities
Post by TenaliRaman on Dec 1^st, 2004, 9:04pm

LOL!!
This reminds me of a discussion i had with a philosophist. During our discussion (math based) we came up with something like this,

Optimistic function : f(x) = abs(x)
Realistic function : f(x) = x
Ignorant function : f(x) = signum(x)
Pessimistic function : f(x) = min(-inf,x)
OverConfident function : f(x) = max(x,inf)

We had more of this , i dont recall well ....
If u were wondering what we were discussing , we were trying to capture emotions in mathematical symbols :D

Title: Re: Integer inequalities
Post by Sir Col on Dec 14^th, 2004, 7:48am

*chuckle* ;D

I love the pessimistic function!

I'm sure we can add a few more to these...

Exaggerating function: f(x)=2x
Boring function: f(x)=0
Unoriginal/copycat function: f(x)=x
[So I suppose that realists are unoriginal copycats!]
Contradictory function: f(x)=-x
Temperamental/unpredicatable/chaotic function: f(z)=z₁₀₀, where z₀=z and z_n+1=z_n²+z₀

Title: Re: Integer inequalities
Post by THUDandBLUNDER on Dec 14^th, 2004, 5:06pm

PMT function: f(x) = sin(1/x)

Title: Re: Integer inequalities
Post by John_Gaughan on Dec 15^th, 2004, 6:41am

PMT function?

on 12/14/04 at 07:48:38, Sir Col wrote:

Temperamental/unpredicatable/chaotic function: f(z)=z₁₀₀, where z₀=z and z_n+1=z_n²+z₀

Interesting function. I wrote a program to calculate the sequence this generates, and noticed some interesting properties. Consecutive values tend to be different by one, with wild variances in the value and sign of numbers.

Code:

#include <iostream>
typedef long long int int64;
int64 f (int64 n)
{
int64 z = n;
for (int64 i = 0; i < 100; ++i)
z = z*z + n;
return z;
}

int main (int argc, char **argv)
{
for (int64 i = (argc > 1 ? atoi (argv[1]) : 0); i <= (argc > 2 ? atoi (argv[2]) : (argc > 1 ? atoi (argv[1]) : -1)); ++i)
std::cout << i << ": " << f (i) << std::endl;
return EXIT_SUCCESS;
}

Edit: I think the sign issue comes from the fact that this thing overflows even 64 bit integers.

Title: Re: Integer inequalities
Post by THUDandBLUNDER on Dec 15^th, 2004, 7:46am

Quote:

PMT function?

Pre
Menstrual
Tension
I thought you said you were married. ;)

Title: Re: Integer inequalities
Post by towr on Dec 15^th, 2004, 11:02am

on 12/15/04 at 06:41:18, John_Gaughan wrote:

It's also related to the Mandelbrot set (http://en.wikipedia.org/wiki/Mandelbrot_set), and basicly forms one of the best known fractals to mankind.

Title: Re: Integer inequalities
Post by John_Gaughan on Dec 15^th, 2004, 11:12am

on 12/15/04 at 07:46:19, THUDandBLUNDER wrote:

Pre
Menstrual
Tension
I thought you said you were married. ;)

I am. Here in the ol' USA we call it PMS: the 'S' stands for "Syndrome."

Title: Re: Integer inequalities
Post by TenaliRaman on Dec 18^th, 2004, 7:06am

Consider f(x) as monotonically decreasing and g(x) as monotonically increasing function ... we form a new function
phi(x) = f(x) + g(x)

This is an altruistic function
;D