41. Problem G: Goldbach's Conjecture Problem G. goldbach's conjecture. Anyway, your task is now to verify Goldbach'sconjecture for all even numbers less than a million. Input Specification. http://www.informatik.uni-ulm.de/acm/Locals/1998/problemset/Goldbach/goldbach.ht

1998/99 ACM International Collegiate Programming Contest University of Ulm Local Contest Problem G Goldbach's Conjecture Input file: goldbach.in In 1742, Christian Goldbach, a German amateur mathematician, sent a letter to Leonhard Euler in which he made the following conjecture: Every even number greater than 4 can be written as the sum of two odd prime numbers. For example: 8 = 3 + 5. Both 3 and 5 are odd prime numbers. Today it is still unproven whether the conjecture is right. (Oh wait, I have the proof of course, but it is too long to write it on the margin of this page.) Anyway, your task is now to verify Goldbach's conjecture for all even numbers less than a million. Input Specification The input file will contain one or more test cases. Each test case consists of one even integer n with Input will be terminated by a value of for n Output Specification For each test case, print one line of the form n = a + b , where a and b are odd primes. Numbers and operators should be separated by exactly one blank like in the sample output below. If there is more than one pair of odd primes adding up to n , choose the pair where the difference b - a is maximized. If there is no such pair, print a line saying "Goldbach's conjecture is wrong."

42. Uncle Petros And Goldbach's Conjecture By Apostolos Doxiadis with amazon.co.uk Genre bookshop authortrekfor new fiction Genre Bookshop underconstant (de)construction Uncle Petros and goldbach's conjecture by Apostolos http://www.geocities.com/SoHo/Nook/1082/uncle_petros.html

for new fiction Genre Bookshop under constant (de)construction Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis This is a highly stimulating novel about the mathematician as artist, following the trend laid down by Simon Singh's 'Fermat's Last Theorem'. And it is attractive to watch artists suffering, as Petros Anargyros does here. For Petros dares solve Goldbach's Conjecture... I do have some literary complaint about Doxiadis though: he makes Petros more romantic than his successful peers, and the narrator writes his account in the style of a math paper. It may as well be a cryptic crossword clue (very apt in the case of one of the mathematicians Doxiadis mentions), with the answer lying in the body of the question. This novel certainly makes you want go out and try and prove Goldbach's Conjecture - you'll wake up in the middle of the night, thinking about it. At first glance, it seems very appropriate that 2 (the only even prime), is mentioned in the conjecture. After all, it's common sense that there can only even be one even prime. If there was an even prime number larger than 2, then it could be divided by 2, and therefore it could not have been prime in the first place. The fact that there is no even prime larger than 2 goes very much in favour of Goldbach's Conjecture, since this discounts a possible exception. However, this is too simplistic. It is not true to say that the higher the even number, the higher the number of pairs of primes. Look at these:

43. Introduction To Arithmetic: Number Theory; Prime Numbers, Fermat Theorem, Goldba Number Theory goldbach's conjecture Fermat's Last Theorem Integers Gaussian IntegersPrime Numbers The Sieve of Eratosthenes The Fundamental Theorem of http://www.geocities.com/mathfair2002/school/arit/arithm3.htm

home stands games about ... links Number Theory Goldbach's Conjecture Fermat's Last Theorem Integers Gaussian Integers Prime Numbers The Sieve of Eratosthenes The Fundamental Theorem of Arithmetic How Many Primes Are There? An Infinity Of Primes Mersenne Numbers Largest Prime Numbers Famous Theorems Diophantine Equations Solving Diophantine Equations Fermat's Last Theorem History of the Theorem Proof Of The Theorem Number Theory Number theory is the branch of mathematics concerned with studying the properties and relations of integers. Many of these problems are concerned with the properties of prime numbers. Number theory also includes the study of irrational numbers, transcendental numbers, Diophantine equations, and continued fractions. There are a number of branches of number theory, including algebraic number theory, analytic number theory, geometric number theory, and probabilistic number theory. Algebraic number theory is the study of numbers that are the roots of polynomial equations with integer coefficients, and includes the study of Gaussian integers. Goldbach's Conjecture One of the most famous problems in number theory is Goldbach's conjecture, proposed in 1742 by Christian Goldbach (1690-1764), the Prussian-born number theorist and analyst, in a letter to Leonhard Euler. Goldbach's conjecture states that any even number greater than or equal to 6 can be expressed as the sum of two odd prime numbers (for example, 6 = 3 + 3, 8 = 5 + 3, 48 = 29 + 19). Although there is every reason to believe that this conjecture is true, and computers have been used to verify it for some very large numbers, it has never been proved. Goldbach's conjecture is a good example of the way in which a problem in number theory can be stated very simply yet be very difficult to solve.

44. Short Story - Goldbach's Conjecture By Brandon M. Stickney - Page 1 Of 7 goldbach's conjecture. goldbach's conjecture (14 ratings) by Brandon M. StickneyPage 1 of 7 goldbach's conjecture. Brandon M. Stickney. http://www.sffworld.com/authors/s/stickney_brandon/fiction/goldbachsconjecture1.

Discussion forum Authors Interviews News ... Support sffworld.com , buy your books through these links Amazon.com Amazon.co.uk or Amazon.de read more Brandon M. Stickney Short Stories Goldbach's Conjecture Goldbach's Conjecture (14 ratings) by Brandon M. Stickney Page 1 of 7 Goldbach's Conjecture Brandon M. Stickney The photo I still have, now brutally folded and fingerprinted, seems to fade, but my own memory is clear, though those who disbelieve now tell me that memory itself cannot be trusted. Memory is an enabler that fills in reality-based details that the mind may be missing and is always ready to employ. If I really saw what I thought I saw, then what I saw was seen among those, other than myself, who refused to see it. It was silver, chrome-a magnetic camouflage hidden among fleeting June clouds and the black sunspots that cluttered my eyes. I still see the awning of my right hand shading my perspective. There as the odd angle of the camera as I brought it up to my eye, and the dizziness that almost toppled me later in my lab. Among the disbelievers, I am untrustworthy I suppose, and as your narrator, I am a guide you need not pay. You can see the photo yourself and your belief, or complacence is payment enough for me, now, after all that has, or has not, happened. Consider yourself saved, if I may be so bold. This began after I had seen it. I wanted to tell her when we were leaving the Red Lobster on Maple Road in Amherst, a suburb thirty miles from Buffalo. I had eaten with Chuck Penney and Page Donohugh, both editors at the

45. Short Story - Goldbach's Conjecture By Brandon M. Stickney - Page 2 Of 7 Short Stories. goldbach's conjecture. goldbach's conjecture (14 ratings)by Brandon M. Stickney goldbach's conjecture was over 200 years old. http://www.sffworld.com/authors/s/stickney_brandon/fiction/goldbachsconjecture2.

Discussion forum Authors Interviews News ... Support sffworld.com , buy your books through these links Amazon.com Amazon.co.uk or Amazon.de read more Brandon M. Stickney Short Stories Goldbach's Conjecture Goldbach's Conjecture (14 ratings) by Brandon M. Stickney Page 2 of 7 "One must show proof that any even number greater than two is the sum of two primes. This is the question." Penney shoved his plate forward, neither hungry nor disappointed, only passionate. Goldbach's Conjecture was over 200 years old. I was familiar with it from a physics geek I roomed with in college. People had been driven mad trying to solve it. More books had been written about the quest for solution than about the solution itself. University classes devoted whole semesters to it. Sabbaticals arranged for the study had wound up alcoholics, suicides, one known double murder, and even a young female professor who simply quit and became a San Francisco prostitute. Through an amorous Italian connection, she wound up posing for Penthouse . It's true. Penney met her when she accompanied philosopher Fran Crick at the '99 Holistic Debunkers Conference, outside Lilydale.

46. VALUE LOGIC: GOLDBACH'S CONJECTURE VALUE LOGIC goldbach's conjecture. “Every even number is the sumof two primes”. Mansur Darlington points out a parallel. “Every http://www.valuelogicmaths.com/description2.htm

VALUE LOGIC: GOLDBACH'S CONJECTURE “Every even number is the sum of two primes” Mansur Darlington points out a parallel             “Every MARRIAGE is the SUM of 2 INDIVIDUALS (indivisibles)” This truism underlines the point that the theme of every ORGANISM (“Jacob’s ladder”) is its UNIQUE evolution from FEELING to MATTER (DNA)  - building its COSMOS by INTERATION of FEELING with every other UNIQUE ORGANISM (Reciprocal Solipsism). Number theory springs from EXPERIENCE – not the other way round ! Our Family “tree” consists of 2 parents, 4 grand parents 2 N   ancestors N generations back.  Our “theme” as an INDIVIDUAL (“prime”) is any “line of descent” we like to choose (see Jacob’s Ladder), and the ramifications from this “theme” which constitute its “three”. Our ancestry which starts as cut and dried rings of “Primes” quickly fades into a Scotch mist when 2 N  becomes big.  This Scotch mist is US – every particle essential to our existence – WE are the living embodiment of our entire “ancestry”. If we draw the first few generations of our ancestry we see that they are concentric circles with us as centre.  Our ancestry (us) is the slice through the ONION model which we carry about with us – it is the COSMOS with TIME squashed flat – the “flat universe”.

47. UNCLE PETROS & GOLDBACH'S CONJECTURE: A NOVEL OF MATHEMATICAL OBSESSION Uncle Petros goldbach's conjecture A Novel of Mathematical Obsession. Goldbach'sConjecture demanded him whole his body, his soul and all of his time. . http://www.acsu.buffalo.edu/~insrisg/bookmarks/bk01/0329petros.htm

A Novel of Mathematical Obsession (This column was first published in the March 29, 2001 ArtVoice of Buffalo.) Mathematicians are very different from the rest of us and even from other members of the scientific research community. I state that from personal experience, having dealt with many of them over a lifetime of work in an activity parallel to but never intersecting theirs. Theirs - and I speak here of world class mathematicians - is an activity so different from that of the rest of us that it is extremely difficult to gain insights into it. Greek author Apostolos Doxiadis has, in (Bloomsbury, 2000), achieved the near impossible. He gives the intelligent outsider a view of what it is like to be on the cutting edge of mathematical research. That he does so in a charming family story, a pleasant tale that holds together the mathematical insights is a further achievement of high order. Here, for example, is how the story begins: "Every family has its black sheep in ours it was Uncle Petros. "My father and Uncle Anargyros, his two younger brothers, made sure that my cousins and I should inherit their opinion of him unchallenged.

48. Uncle Petros And Goldbach's Conjecture : Apostolos Doxiadis , UNCLE PETROS and goldbach's conjecture Apostolos Doxiadis. Perfection.Uncle Petros and goldbach's conjecture . . . Apostolos Doxiadis. http://faylicity.com/book/book1/petros.html

UNCLE PETROS and GOLDBACH'S CONJECTURE : Apostolos Doxiadis ÁÕ¤Ó¡ÅèÒÇäÇéÇèÒ A mathematician is born, not made. ¹Ñ¡¤³ÔµÈÒʵì¹Ñé¹à¡Ô´ÁÒà¾×èͨÐà»ç¹ÍÂèÒ§¹Ñé¹ äÁèä´é¶Ù¡ÊéÒ§¢Öé¹ à»â´Ê à»ç¹Ë¹Öè§ã¹¼Ùé·ÕèÁÕ¤ÇÒÁÊÒÁÒ¶¾ÔàÈÉà¾×èͨÐà¡Ô´ÁÒà»ç¹¹Ñ¡¤³ÔµÈÒÊµì ¹Ç¹ÔÂÒÂàÅèÁ¹Õéà»ç¹à×èͧ¢Í§à»â´Ê¡Ñº»Ñ­ËÒ·Ò§¤³ÔµÈÒʵì·Õèà¢Ò·ØèÁà·ªÕÇÔµãËé à»â´Ê¹Ñé¹à»ç¹µÑÇÅФ·ÕèÊéÒ§¢Öé¹ áµè»Ñ­ËÒ·Õèà¢Ò¾ÂÒÂÒÁ¤Ô´·Ò§á¡é¹Õéà»ç¹»Ñ­ËÒ·ÕèÁÕµÑǵ¹¨Ô§·Ò§¤³ÔµÈÒÊµì »Ñ­ËÒ¢é͹Õéà»ç¹·ÕèÙé¨Ñ¡¡Ñ¹´Õà¾ÒÐà»ç¹»ÔȹÒà¡èÒá¡è¡ÇèÒ 250 »Õ ·Õè¹Ñ¡¤³ÔµÈÒʵìÂѧ¾ÔÊÙ¨¹ìäÁèä´é¨¹ºÑ´¹Õé ª×èͧ͢»Ñ­ËÒ¹ÕéàÕ¡¡Ñ¹ÇèÒ Goldbach's Conjecture ·Õè¤ÔÊàµÕ¹ â¡Å´ìºÒ¤ (1690-1764) à¢Õ¹¶Ö§ÍÍÂàÅÍì (Euler 1707-1783) ã¹»Õ 1742 ÁÕ¤ÇÒÁµÍ¹Ë¹Öè§ÇèÒ "¨Ó¹Ç¹àµçÁã´æ ·ÕèÁÒ¡¡ÇèÒ 5 ÊÒÁÒ¶áÊ´§ã¹Ù»¼ÅºÇ¡¢Í§¨Ó¹Ç¹à©¾ÒÐ 3 µÑÇä´é" [¨Ó¹Ç¹à©¾ÒФ×ͨӹǹàµçÁÁÒ¡¡ÇèÒ 1 ·ÕèäÁèÁÕÍÐäËÒÁѹä´éŧµÑǹ͡¨Ò¡ 1 áÅеÑÇÁѹàͧ àªè¹ 2,3,5,7,11,13,17] «Öè§ËÒ¡¾Ô¨Ò³Òáµè¨Ó¹Ç¹àµçÁ·Õèà»ç¹àÅ¢¤ÙèáÅéÇ áÅШҡ¢éÍà·ç¨¨Ô§ÇèÒ àÅ¢¤Õè + àÅ¢¤Õè = àÅ¢¤Ùè áÅÐàÁ×èͨӹǹ੾ÒзÕèà»ç¹àÅ¢¤ÙèÁÕáµè 2 µÑÇà´ÕÂÇà·èÒ¹Ñé¹ ´Ñ§¹Ñé¹ÍÍÂàÅÍì¨Ö§àÕºàÕ§»Ð⤢éÒ§µé¹ãËÁè ÇèÒ áÅйÕèàͧ¤×ÍÊÔ觷ÕèàÕ¡¡Ñ¹ÇèÒ Goldbach's Conjecture µÑÇÍÂèÒ§àªè¹ 10 = 3+7 6,701,058 = 641 + 6,700,417

49. Uncle Petros And Goldbach's Conjecture ºÒ§µÍ¹ UNCLE PETROS and goldbach's conjecture Apostolos Doxiadis. One ×¹à×͹ ªÑé¹Ë¹Ñ§Ê×Í Uncle Petros and goldbach's conjecture. http://faylicity.com/book/book1/fstpetros.html

Uncle Petros and Goldbach's Conjecture UNCLE PETROS and GOLDBACH'S CONJECTURE : Apostolos Doxiadis One Every family has its black sheep - in ours it was Uncle Petros. My father and Uncle Anargyros, his two younger brothers , made sure that my cousins and I should inherit their opinion of him unchallenged. 'That no-good brother of mine, Petros, is one of life's failure,' my father would say at every opportunity. And Uncle Anargyros, during the family get-togethers from which Uncle Petros routinely absented himself, always accompanied mention of his name with snorts and grimaces expressing disapproval, disdain or simple resignation, depending on his mood. However, I must say this for them: both brothers treated him with scrupulous fairness in financial matters. Despite the fact that he never shared even a slight part of the labour and the responsibilities involved in running the factory that the three inherited jointly from my grandfather, Father and Uncle Anargyros unfailingly paid Uncle Petros his share of the profits. (This was due to a strong sense of family, another common legacy.) As for Uncle Petros, he repaid them inthe same measure. Not having had a family of his own, upon his death he left us, his nephews, the children of his magnanimous brothers, the fortune that had been multiplying in his bank account practically untouched in its entirety. Specially to me, his 'most favoured of nephew' (his own words), he additionally bequeathed his huge library which I, in turn, donated to the Helleinic Mathematical Society. For myself I retained only two of its items, volume seventeen of Leonard Euler's

50. Bidworth Auction - Proof Of Goldbach's Conjecture Proof of goldbach's conjecture. http://www.bidworth.com/Bidworth/Books.nsf/9041cf3699a0a0c7802566c4005bf8c3/1b69

51. [math/0005185] A Proof Of "Goldbach's Conjecture" 26 Jan 2001 200428 GMT (43kb) A Proof of goldbach's conjecture .Authors Roger Ellman (TheOrigin Foundation, Inc) Comments 8 http://arxiv.org/abs/math.GM/0005185

Mathematics, abstract math.GM/0005185 ): Thu, 18 May 2000 18:07:50 GMT (43kb) Date (revised v2): Fri, 26 Jan 2001 20:04:28 GMT (43kb) A Proof of "Goldbach's Conjecture" Authors: Roger Ellman (The-Origin Foundation, Inc) Comments: 8 pages, change is non-material editing Subj-class: General Mathematics "Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers. Full-text: PDF only References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Links to: arXiv math find abs

52. Goldbach Biography, with links to other Goldbach resources.Category Science Math Open Problems Goldbach Conjecture...... Other references in MacTutor. Chronology 1740 to 1760.Other Web sites, The Prime Pages (goldbach's conjecture); http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Goldbach.html

53. Comments About MacTutor History Archive goldbach's conjecture that “Every even number N?4 can be expressed as the sumof two primes” was first stated in 1742 in a letter of Christian Goldbach http://www-gap.dcs.st-and.ac.uk/~history/Comments/comments.html

54. The Prime Page's Links++: Theory/conjectures/Goldbach Numbers Add Update New Popular . goldbach's conjecture suggeststhat every even number greater than 2 is the sum of two primes. http://primes.utm.edu/links/theory/conjectures/Goldbach/

Links related to Prime Numbers Add Update New Popular Goldbach's conjecture suggests that every even number greater than 2 is the sum of two primes. Top theory conjectures : Goldbach Resources in theory : conjectures : Goldbach $1,000,000 prize for proof - The publisher's rules limit participation to residents of the United Kingdom and the United States who are 18 years or older. The deadline for entries is March 2002. (Added: 20-Aug-2000 Hits: 379 Rating: 10.00 Votes: 1) Rate It Goldbach Conjecture Research - Introduction, graphs, history and more... (Added: 20-Aug-2000 Hits: 772 Rating: 9.00 Votes: 3) Rate It Goldbach's conjecturerecent progress - We summarize some recent progress in proving Goldbach's conjecture, giving conjectured asymptotic formulas. (Added: 20-Aug-2000 Hits: 614 Rating: Votes: 0) Rate It Goldbach's Prime Pairs - Very nice introduction to Goldbach's conjecture and Jörg Richstein's verification to 4 x 10 (Added: 20-Aug-2000 Hits: 423 Rating: Votes: 0) Rate It Mathematical mysteries: the Goldbach conjecture - Definition plus simple calculator to find pairs of primes that add to the integer you input. (Added: 20-Aug-2000 Hits: 380 Rating: Votes: 0) Rate It Prime Glossary's entry (Added: 20-Aug-2000 Hits: 148 Rating: Votes: 0) Rate It Verifying Goldbach's Conjecture up to 4 x 10 - Definition, list of previous calculations, nice bibliography and notes about the verification to 4 x 10

55. The Prime Glossary: Odd Goldbach Conjecture There has been substantial progress on the odd Goldbach conjecture, theeasier case of goldbach's conjecture. See Also goldbach's conjecture. http://primes.utm.edu/glossary/page.php?next=number of divisors

56. Re: Goldbach's Conjecture - The Various Definitions Re goldbach's conjecture the various definitions. goldbach's conjecture statesthat any EVEN OR ODD number can be expressed by a sum of three primes. http://www.inet-one.com/cypherpunks/dir.1998.11.23-1998.11.29/msg00028.html

CH recommended: Buy This Book! Buy This Book! Date Prev Date Next Thread Prev Thread Next ... Subject Index Re: Goldbach's Conjecture - the various definitions To ravage@EINSTEIN.ssz.com Subject : Re: Goldbach's Conjecture - the various definitions From apf2@apf2.com Date : Tue, 24 Nov 1998 06:03:43 +0100 Cc cypherpunks@cyberpass.net In-Reply-To Sender owner-cypherpunks@Algebra.COM Prev by Date: RealSystem G2 Ships Next by Date: Re: Goldbach's Conjecture - the various definitions (fwd) Prev by thread: RealSystem G2 Ships Next by thread: Re: Goldbach's Conjecture - the various definitions (fwd) Index(es): Date Thread Author Subject

57. Re: Goldbach's Conjecture - The Various Definitions (fwd) Thread Next Date Index Thread Index Author Index Subject IndexRe goldbach's conjecture the various definitions (fwd). http://www.inet-one.com/cypherpunks/dir.1998.11.23-1998.11.29/msg00029.html

Date Prev Date Next Thread Prev Thread Next ... Subject Index Re: Goldbach's Conjecture - the various definitions (fwd) To cypherpunks@EINSTEIN.ssz.com (Cypherpunks Distributed Remailer) Subject : Re: Goldbach's Conjecture - the various definitions (fwd) From ravage@EINSTEIN.ssz.com Date : Mon, 23 Nov 1998 16:53:10 -0600 (CST) Sender owner-cypherpunks@Algebra.COM Prev by Date: Re: Goldbach's Conjecture - the various definitions Next by Date: building a better zyklon-B (Re: KRA on ADK vs KR, NAI membership) Prev by thread: Re: Goldbach's Conjecture - the various definitions Next by thread: building a better zyklon-B (Re: KRA on ADK vs KR, NAI membership) Index(es): Date Thread Author Subject

58. MATHS300: Goldbach's Conjecture Overview MATHS300 Lesson 105. home. goldbach's conjecture. Overview. Each MATHS300lesson serves two purposes. On the one hand it is a professional http://www.blackdouglas.com.au/maths300/m300over/105ogold.htm

Lesson 105 Goldbach's Conjecture Overview Each MATHS300 lesson serves two purposes. On the one hand it is a professional development experience offering opportunity to try something new, hopefully in conjunction with your staff, in the knowledge that the notes record the successful experiences of your colleagues elsewhere. On the other hand it is a well trialed lesson plan which provides clear information about 'what to do in maths tomorrow'. Years Time : 1 - 2 lessons Summary: 8 = 5 + 3 and 10 = 7 + 3 and 12 = 7 + 5. What is common to all these additions? It is that an even number is the sum of two prime numbers. This is the conjecture attributed to Goldbach (a Prussian mathematician, 1690 - 1764) and which bears his name. In this lesson, it is presented as the investigative challenge: Can every even number greater than 4 be written as the sum of two primes? The lesson is essentially about recognising prime numbers and it includes much skill practice in addition. However, the investigation and genuine history behind the challenge gives it a richness beyond just skill practice. There are several lessons of a similar genre within Maths 300. Some of these are:

59. Uncle Petros And Goldbach's Conjecture Uncle Petros and goldbach's conjecture and other books by Apostolos Doxiadis. Availablefrom Penguin Books Canada Dev. Uncle Petros and goldbach's conjecture, http://www.penguin.ca/Book/BookDisplay/0,1008,0571205119,00.html

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60. Count On - The Sum Newpaper PUBLISHING giant Faber and Faber is offering a prize of one million dollars to anyonewho can prove the theory known as goldbach's conjecture within the next http://www.mathsyear2000.org/thesum/issue4/sunbottom.html

Prize Sparks Goldbach Fever PUBLISHING giant Faber and Faber is offering a prize of one million dollars to anyone who can prove the theory known as Goldbach's Conjecture within the next two years. The offer is part of the publicity drive for a new book by a Greek mathematician and author Apostolos Doxiadis called Uncle Petros and Goldbach's Conjecture in which a man dedicates his life to the challenge. The book has already been translated into 15 languages and Faber has high hopes of it becoming a bestseller, given the recent success of stories about great scientific quests like Dava Sovel's Longitude and Simon Singh's Fermat's Last Theorem. If you don't know what Goldbach's Conjecture is, see the box below. If you do, then there is a chance you may want to throw your hat into the ring and have a shot at the million dollar prize. Be warned though, the proof has to be published by a respectable mathematical journal within two years and proved correct by Faber's panel of experts. Faber has spent a five-figure sum insuring itself again a pay-out, but boss Tony Faber said he would be happy to hand over the prize. He said: "Now that we are insured, I'd love it if someone won."

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