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#1




Did anyone ever participate in the Putnam math competition? What'd you think?
I'd never heard of this competition until my son participated. (I wasn't a math geek, so it's not too surprising, though I spent so much time at MIT mooning after nerds you'd think I would have at least known about it.) My son enjoyed it and will keep doing it, even though his score wasn't high enough to confer any bragging rights.
Seems like it could be fun for the right kind of person. Anyone on the SD ever do it?
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If I waited for memory to serve, I'd starve. 
#2




Back when I was in college I heard about it. Thought about it, but never did it. But my college had an annual mathematics competition and I did that twice. Fun and interesting. I placed 3rd my first year, and then 2nd the next year, and won a little money. Math competitions are fun because you use your bag of tricks to solve problems, and the problems can be solved using different methods. You got points for elegance, too. It was a great experience. I was a bit of a math geek back then. Not especially good at it, but I enjoyed it.
Sounds like the CairoKid likes it! It's something he can put on his resumé. Last edited by Bullitt; 10132017 at 06:33 AM. 
#3




The Putnam is generally accepted among math people as having the most nerd cred. If your son has any plans of going into a STEM career, a good Putnam score could give him a leg up. Even if he doesn't, as long as he's enjoying it, it should be encouraged. The Putnam is one of the few remaining academic tests where even the top scorers get a miserable low mark and I feel tests like that are important for young people to experience.

#4




I hadn't thought of that, but you make a very good point.
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If I waited for memory to serve, I'd starve. 


#5




My nephew does the Scottish maths challenge and does well at it.
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Quartz 
#6




I didn't participate but I knew people who did in college. I think they all got 5 points or less.
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Sometimes I doubt your commitment to sparkle motion Last edited by Wesley Clark; 10132017 at 08:54 AM. 
#7




Considering the median score is 1 (out of 120), a 5 is a very good score!

#8




Quote:
Edit, nope. median score is 01. I can't remember what my friends and acquaintances got, but they seemed to get 0 or 1 on most of the questions. No 10s for any of them for what I remember.
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Sometimes I doubt your commitment to sparkle motion Last edited by Wesley Clark; 10132017 at 05:26 PM. 
#9




I took it twice. I scored 6 or 7 points the first time, and the secretary who gave me my score sort of apologized, but I was happy. The second time, my boyfriend coached me a little about the importance of elegance (or at least, not leaving loose ends all over the place) and I doubled my score.
It was a good experience. 


#10




How is it scored?
Also, I found some sample questions here. My high school/collegelevel math concepts and vocabulary are frankly pitiful, so I don't even understand how to start most of them. But I think I have one of them (okay, in typing it out I realize I don't understand it as well as I thought and would love some help): Quote:
SPOILER:

#12




Quote:
SPOILER:
The third problem has an easy solution I think: SPOILER:

#13




I never took it. I was supposed to but the professor who was supposed to apply for us missed the deadline. But I have looked over the questions regularly and they are very hard. Even as a professional mathematician, I doubt I would get a very high score. For example, I just read the question posed by LHoD and I would not have the foggiest idea how to get started. I think his solution is correct, although I have not thought it through thoroughly.
There are two parts. The first part consists of questions that many will get. I can usually do about half of them. The second part is much harder and I cannot usually do any of them. The team that won the very first Putnam in the 1930s was from U. of Toronto and, over the years, I met all three members. One was an absolutely brilliant mathematician, arguably the top American mathematician of his era (he spent his entire career in the US). The second member was a decent enough mathematician, nothing spectacular, and the third was a cipher. So it is hard to know what the significance of winning is. I guess it rewards a certain kind of quickness, rather than the steady growth of understanding that always characterized my research. 
#14






#15




That explanation makes total sense to me, and is pretty cool. Thanks!

#16




I did the Putnam once or twice. I thought it was kind of fun, although I didn't distinguish myself (I can't remember my scores, but probably less than 10). It eats up a whole day, though!
My math contest skills peaked in grade 11 when I did well in the Fermat competition. 
#17




That wouldn't be optimal play by B...
SPOILER:

#18




I am in the "I heard about the Putnam, but never actually tried it in college" group.
If calculus and really highlevel stuff throws you, try the USA Mathematical Olympiad questions  six questions in two groups of three, with 4 1/2 hours allowed per group, and no calculus. Archive of past USAMO questions For those of us who do much better with numbercrunching problems than proofs, the next level down is the American Invitational Mathematics Exam (in order to be eligible to take it, you need to score 100 or more on the AMC 12 exam, formerly known as the AHSME, but my high school teachers always called it "the MAA exam") Archive of past AIME questions 
#19




So yeah: no, I never entered the Putnam Math Competition.



#20




I hadn't heard of it.
In high school we had a Math League. Once a month we went to another high school and took a one hour test with ten questions. You had to give them precisely the correct answer they wanted. Questions were Putnamlike, but a couple steps down in difficulty. I don't think I ever scored above 5 or 6. One time they gave an advanced math test at my high school. I think it was on a state level. There were more problems than at a Math League meet, and you got more than an hour. I don't know which test it was.
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“Of course,” said my grandfather, stepping from the Time Machine and pulling a gun from his belt, “There’s no paradox if I shoot you!” 
#21




Quote:
For DPRK, k = (n/2), and I'll tweak it just a little: SPOILER:
But I'm not sure if DPRK's is a definitive proof. Is it? For all n? The following shows that B always wins for n = 1 and for n = 2. Furthermore, for n = 1 and n = 2, it is impossible for A to win. B must be the winner, even if B can misplay its hand. For n = 1, regardless of what A plays, either a 1 or a 2 (the only cards in the deck), B's play results in Σ = 3 and B wins. Trivial, but important to show. If it is true that the same player must win regardless of n, then this proves B always wins for any n, because B wins for n = 1, and the proof is complete. Continuing, for n = 2, A can have one of six possible hands: (1,2), (1,3), (1,4), (2,3), (2,4), and (3,4).
A(1,4) is just a little more complicated...
Similarly for A(2,3), A(2,4), and A(3,4), B always wins:
Therefore, for n = 2, B always wins. Not only that, but A can never win  B must win, even if B misplays the game. This is a brute force approach. There's probably a more elegant proof! 
#22




My current understanding:
The way the game is written, for any particular nonwinning sum at the end of my turn, my opponent has one theoretical card that can be played to win. If there are ten cards, if I end my turn at 11, I win; but if I end it at 12, my opponent must play a 10 to win, and if I end at 13, they must play a 9, and so on. Call the sum at the end of my turn the "endsum"; the card I play is the "sum determiner"; the card they must play to win is the "winning card." Each card is unique. I can choose among my cards which sum determiner to play, giving a unique endsum for each choice, and requiring a unique winning card. I have one more sum determiner than they have potential winning cards. If I have five cards left in my hand, that's five different possible end sums. And they only have four cards. I can choose the end sum for which they lack the winning card. 
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