solution to the puzzle

Solution to puzzle: Two logicians
Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.S: I knew that.P: Now I can determine them.S: So can I.


Given that the above statements are true, what are the two numbers?
First of all, trivially, xy cannot be prime. It also cannot be the square of a prime, for that would imply x = y.
We now deduce as much as possible from each of the logicians' statements. We have only public information: the problem statement, the logicians' statements, and the knowledge that the logicians, being perfect, will always make correct and complete deductions. Each logician has, in addition, one piece of private information: sum or product.
P: I cannot determine the two numbers.
P's statement implies that xy cannot have exactly two distinct proper factors less than 100.Call such a pair of factors eligible.
For example, xy cannot be the product of two distinct primes, for then P could deduce the numbers. Likewise, xy cannot be the cube of a prime, such as 33 = 27, for then 3×9 would be a unique factorization; or the fourth power of a prime.
Other combinations are ruled out by the fact that the sum of the two factors must be less than 100. For example, xy cannot be 242 = 2×112, since 11×22 is the unique eligible factorization; 2×121 being ineligible. Similarly for xy = 318 = 2×3×53.
S: I knew that.
If S was sure that P could not deduce the numbers, then none of the possible summands of x+y can be such that their product has exactly one pair of eligible factors. For example, x+y could not be 51, since summands 17 and 34 produce xy = 578, which would permit P to deduce the numbers.
We can generate a list of values of x+y that are never the sum of precisely two eligible factors.
genSum(100);
eligiblesums: 11, 17, 23, 27, 29, 35, 37, 41, 47, 53.
(We can usegold bach conjecture ie. even integer greater than 2 can be expressed as the sum of two primes, to deduce that the above list can contain only odd numbers. Although the conjecture remains unproven, it has been confirmed empirically up to 3×1017.)
P: Now I can determine them.
P now knows that x+y is one of the values listed above. If this enables P to deduce x and y, then, of the eligible factorizations of xy, there must be precisely one for which the sum of the factors is in the list. The table below, , shows all such xy, together with the corresponding x, y, and x+y. The table is sorted by sum and then product.
Note that a product may be absent from the table for one of two reasons. Either none of its eligible factorizations appears in the above list of eligible sums (example: 12 = 2×6 and 3×4; sums 8 and 7), or more than one such factorization appears (example: 30 = 2×15 and 5×6; sums 17 and 11.)
S: So can I.
If S can deduce the numbers from the table below, there must be a sum that appears exactly once in the table. Checking the table, we find just one such sum: 17.Therefore, we are able to deduce that the numbers are x = 4 and y = 13.

n.b. i am sorry the table could be published as some error is occuring but i think u will be able to figure out the solution after this....

kurt cobain...we miss you

the Suicide Note of Kurt Donald Cobain, 1967-1994

---

To Boddah

Speaking from the tongue of an experienced simpleton who obviously would rather be an emasculated, infantile complain-ee. This note should be pretty easy to understand.

All the warnings from the punk rock 101 courses over the years, since my first introduction to the, shall we say, ethics involved with independence and the embracement of your community has proven to be very true. I haven't felt the excitement of listening to as well as creating music along with reading and writing for too many years now. I feel guity beyond words about these things.

For example when we're back stage and the lights go out and the manic roar of the crowds begins., it doesn't affect me the way in which it did for Freddie Mercury, who seemed to love, relish in the the love and adoration from the crowd which is something I totally admire and envy. The fact is, I can't fool you, any one of you. It simply isn't fair to you or me. The worst crime I can think of would be to rip people off by faking it and pretending as if I'm having 100% fun. Sometimes I feel as if I should have a punch-in time clock before I walk out on stage. I've tried everything within my power to appreciate it (and I do,God, believe me I do, but it's not enough). I appreciate the fact that I and we have affected and entertained a lot of people. It must be one of those narcissists who only appreciate things when they're gone. I'm too sensitive. I need to be slightly numb in order to regain the enthusiasms I once had as a child.

On our last 3 tours, I've had a much better appreciation for all the people I've known personally, and as fans of our music, but I still can't get over the frustration, the guilt and empathy I have for everyone. There's good in all of us and I think I simply love people too much, so much that it makes me feel too fucking sad. The sad little, sensitive, unappreciative, Pisces, Jesus man. Why don't you just enjoy it? I don't know!

I don't have a goddess of a wife who sweats ambition and empathy... and a daughter who reminds me too much of what i used to be, full of love and joy, kissing every person she meets because everyone is good and will do her no harm. And that terrifies me to the point to where I can barely function. I can't stand the thought of Frances becoming the miserable, self-destructive, death rocker that I've become.

I have it good, very good, and I'm grateful, but since the age of seven, I've become hateful towards all humans in general. Only because it seems so easy for people to get along that have empathy. Only because I love and feel sorry for people too much I guess.

Thank you all from the pit of my burning, nauseous stomach for your letters and concern during the past years. I'm too much of an erratic, moody baby! I don't have the passion anymore, and so remember, it's better to burn out than to fade away.

Peace, love, empathy.

Kurt Cobain

Frances and Courtney, I'll be at your alter.
Please keep going Courtney, for Frances.
For her life, which will be so much happier without me.

I LOVE YOU, I LOVE YOU!

nice puzzle

Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that the above statements are true, what are the two numbers?
answers will be given next week.

beauty and the beast

stopping by the woods on a snowy evening

Whose woods these are I think I know.
His house is in the village, though;
He will not see me stopping here
To watch his woods fill up with snow.

My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.

He gives his harness bells a shake
To ask if there is some mistake.
The only other sound's the sweep
Of easy wind and downy flake.

The woods are lovely, dark, and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.

mathematics

Well this is my first posting in blogs.....i have not opened this page for my friends,foes and any other people...its like many other people i would be writing down my thoughts....there are two things that i love the most...first is my girlfriend monalisa and second is mathematics..