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Topic: Integer inequalities (Read 1127 times) |
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NickH
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Integer inequalities
« on: Nov 30th, 2004, 2:44pm » |
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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.)
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towr
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Re: Integer inequalities
« Reply #1 on: Nov 30th, 2004, 3:43pm » |
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Maybe I'm getting it wrong, but there doesn't seem to be a solution..
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NickH
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Re: Integer inequalities
« Reply #2 on: Nov 30th, 2004, 4:38pm » |
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Quote:| Maybe I'm getting it wrong, but there doesn't seem to be a solution.. |
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There is definitely a solution!
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Aryabhatta
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Re: Integer inequalities
« Reply #3 on: Nov 30th, 2004, 4:57pm » |
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is it 1,5,7,10 ?
Found it easier to work putting B = A-X, C = A-Y and D = A-Z and finding possible values of X,Y,Z.
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Grimbal
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Re: Integer inequalities
« Reply #5 on: Dec 1st, 2004, 2:32am » |
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Positive integers!
::A,B,C,D = 10,7,5,1::
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towr
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Re: Integer inequalities
« Reply #6 on: Dec 1st, 2004, 7:02am » |
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I'm an optimist, I consider everything that's not negative positive 
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Aryabhatta
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Re: Integer inequalities
« Reply #7 on: Dec 1st, 2004, 11:27am » |
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on Dec 1st, 2004, 7:02am, towr wrote:| I'm an optimist, I consider everything that's not negative positive |
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Wouldn't that make you a realist?
An optimist would consider even a negative as positive.. 
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TenaliRaman
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Re: Integer inequalities
« Reply #8 on: Dec 1st, 2004, 9:04pm » |
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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 
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Sir Col
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Re: Integer inequalities
« Reply #9 on: Dec 14th, 2004, 7:48am » |
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*chuckle*
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 zn+1=zn2+z0
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ThudnBlunder
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Re: Integer inequalities
« Reply #10 on: Dec 14th, 2004, 5:06pm » |
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PMT function: f(x) = sin(1/x)
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John_Gaughan
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Re: Integer inequalities
« Reply #11 on: Dec 15th, 2004, 6:41am » |
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PMT function?
on Dec 14th, 2004, 7:48am, Sir Col wrote:
Temperamental/unpredicatable/chaotic function: f(z)=z100, where z0=z and zn+1=zn2+z0 |
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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;
} |
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Edit: I think the sign issue comes from the fact that this thing overflows even 64 bit integers.
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| « Last Edit: Dec 15th, 2004, 6:42am by John_Gaughan » |
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x = (0x2B | ~0x2B)
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ThudnBlunder
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Re: Integer inequalities
« Reply #12 on: Dec 15th, 2004, 7:46am » |
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Quote:
Pre
Menstrual
Tension
I thought you said you were married.
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| « Last Edit: Dec 15th, 2004, 7:49am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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towr
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Re: Integer inequalities
« Reply #13 on: Dec 15th, 2004, 11:02am » |
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on Dec 15th, 2004, 6:41am, John_Gaughan wrote:| 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. |
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It's also related to the Mandelbrot set, and basicly forms one of the best known fractals to mankind.
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| « Last Edit: Dec 15th, 2004, 11:04am by towr » |
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John_Gaughan
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Behold, the power of cheese!
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Re: Integer inequalities
« Reply #14 on: Dec 15th, 2004, 11:12am » |
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on Dec 15th, 2004, 7:46am, THUDandBLUNDER wrote:Pre
Menstrual
Tension
I thought you said you were married. |
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I am. Here in the ol' USA we call it PMS: the 'S' stands for "Syndrome."
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x = (0x2B | ~0x2B)
x == the_question
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TenaliRaman
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I am no special. I am only passionately curious.
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Re: Integer inequalities
« Reply #15 on: Dec 18th, 2004, 7:06am » |
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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
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