Claim: Student mistakes examples of unsolved math problems for homework assignment and solves them.
TRUE 
Example: [Brunvand, 1987]
A young college student was working hard in an upperlevel math course, for fear that he would be unable to pass. On the night before the final, he studied so long that he overslept the morning of the test.
When he ran into the classroom several minutes late, he found three equations written on the blackboard. The first two went rather easily, but the third one seemed impossible. He worked frantically on it until — just ten minutes short of the deadline — he found a method that worked, and he finished the problems just as time was called.
The student turned in his test paper and left. That evening he received a phone call from his professor. "Do you realize what you did on the test today?" he shouted at the student.
"Oh, no," thought the student. I must not have gotten the problems right after all.
"You were only supposed to do the first two problems," the professor explained. "That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!"
When he ran into the classroom several minutes late, he found three equations written on the blackboard. The first two went rather easily, but the third one seemed impossible. He worked frantically on it until — just ten minutes short of the deadline — he found a method that worked, and he finished the problems just as time was called.
The student turned in his test paper and left. That evening he received a phone call from his professor. "Do you realize what you did on the test today?" he shouted at the student.
"Oh, no," thought the student. I must not have gotten the problems right after all.
"You were only supposed to do the first two problems," the professor explained. "That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!"
Origins: This legend combines one of the ultimate academic wishfulfillment
One day In 1939,
George Dantzig recounted his feat in a 1986 interview for the College Mathematics Journal:
It happened because during my first year at Berkeley I arrived late one day at one of [Jerzy] Neyman's classes. On the blackboard there were two problems that I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework — the problems seemed to be a little harder than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o'clock, [my wife] Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.
A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
The second of the two problems, however, was not published until after WorldWar II. It happened this way. Around 1950 I received a letter from Abraham Wald enclosing the final galley proofs of a paper of his about to go to press in the Annals of Mathematical Statistics. Someone had just pointed out to him that the main result in his paper was the same as the second "homework" problem solved in my thesis. I wrote back suggesting we publish jointly. He simply inserted my name as coauthor into the galley proof.
Dr. Dantzig also explained how his story passed into the realm of urban legendry:
A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis.
The second of the two problems, however, was not published until after World
The other day, as I was taking an early morning walk, I was hailed by Don Knuth as he rode by on his bicycle. He is a colleague at Stanford. He stopped and said, "Hey, George — I was visiting in Indiana recently and heard a sermon about you in church. Do you know that you are an influence on Christians of middle America?" I looked at him, amazed. "After the sermon," he went on, "the minister came over and asked me if I knew a George Dantzig at Stanford, because that was the name of the person his sermon was about."
The origin of that minister's sermon can be traced to another Lutheran minister, the Reverend Schuler [sic] of the Crystal Cathedral inLos Angeles. He told me his ideas about thinking positively, and I told him my story about the homework problems and my thesis. A few months later I received a letter from him asking permission to include my story in a book he was writing on the power of positive thinking. Schuler's published version was a bit garbled and exaggerated but essentially correct. The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.
The version of Dantzig's story published by Robert Schuller contained a good deal of embellishment and misinformation which has since been propagated in urban
The origin of that minister's sermon can be traced to another Lutheran minister, the Reverend Schuler [sic] of the Crystal Cathedral in

George Dantzig (himself the son of a mathematician) received a Bachelor's degree from University of Maryland in 1936 and a Master's from the University of Michigan in 1937 before completing his Doctorate (interrupted by World
George Dantzig passed away at his Stanford home at age 90 on
Sightings: This legend is used as the setup of the plot in the 1997 movie
Last updated: 23 September 2014
Sources: 
Albers, Donald J. and Constance Reid.  "An Interview of George B. Dantzig: The Father of Linear Programming."
College Mathematics Journal. Volume 17, Number 4; 1986 (pp. 293314). Brunvand, Jan Harold. Curses! Broiled Again! New York: W. W. Norton, 1989. ISBN 0393307115 (pp. 278283).  Dantzig, George B.

"On the NonExistence of Tests of 'Student's' Hypothesis Having Power Functions  Independent of Sigma."
Annals of Mathematical Statistics. No. 11; 1940 (pp. 186192). Dantzig, George B. and Abraham Wald. "On the Fundamental Lemma of Neyman and Pearson." Annals of Mathematical Statistics. No. 22; 1951 (pp. 8793). Pearce, Jeremy. "George B. Dantzig Dies at 90." The New York Times. 23 May 2005.