8 ms·
Are You Smarter Than a Quant? Questions from the MoMath Masters Contest
- ikeboy 11y agoI got all except 4, which is trivia. (Well 1 is sort of trivia as well, but I happened to know that Fermat proved that one).
- pflats 11y agoI somehow dug Cindy out of the crypts of my brain. The squeeze theorem is sometimes also called the sandwich theorem, so that one threw me off. It's also sometimes (in Italian and Russian, according to my professors) called the Theorem of The Two Policemen. Imagine the path of a drunk staggering down the street. Then imagine the path of the two cops who come to grab him by the shoulders. Et voila! The Theorem of the Two Policemen.
- zem 11y ago> The squeeze theorem is sometimes also called the sandwich theorem, so that one threw me off. E is also the "ham sandwich theorem", so it looks like they were going for deliberately confusing
- valine 11y agoProblem 5 was fun. My solution was less complex: if (((i * i) + 7 * i + 89) % 77 == 0) System.out.print(i);
- Bahamut 11y agoThat's cheating though - also it likely is faster to do it mentally than typing all that out for the brightest.
- valine 11y agoThat's probably fair. It likely would have taken me a minute to do the mental math. The burst force approach took 15 seconds of typing and very little mental effort.
- harryh 11y agoI think the real answer is that in the competition only pencil & paper is allowed. No computers.
- S4M 11y agoThey are using tablets on the pictures. Surely those have calculators.
- harryh 11y agoI think those are the source of the questions? But ya, you might be right.
- tromp 11y agoThe ipads are locked down to run the contest app. Besides, calculators have rather poor programming support...
- jerf 11y ago"Speak for your self" said the HP-48 owner, tapping into a decades-old bank of accumulated smug. Mmmmmm... delicious, delicious RPN smug. I haven't tasted this in years. Not as fresh as it used to be, but still sweet.
- deleted 11y ago[deleted]
- deleted 11y ago[deleted]
- owenversteeg 11y agoNot a fan of the questions. 1) is trivia/trick question (obviously designed to catch those who learned the squeeze theorem as the sandwich theorem), 2) is hilariously simple, 3) is trivial, 4) is trivia, 5) is interesting. Anyone have access to the harder, non-trivia(l) questions please? [edit] found a few more from 2013, which I think are more interesting: http://digitaleditions.walsworthprintgroup.com/display_article.php?id=1461361 http://digitaleditions.walsworthprintgroup.com/display_artic...
- parennoob 11y ago> obviously designed to catch those who learned the squeeze theorem as the sandwich theorem Shouldn't the "Fermat" part rule out the squeeze theorem? I know Fermat did work that contributed to the development of Calculus, but he was gone long before either Newton or Leibniz published.
- danbruc 11y agoThe last one is trivial, too. Is 8 x 8 + 7 x 8 + 89 = 209 divisible by 77? Nope. Is 18 x 18 + 7 x 18 + 89 = 539 divisible by 77? Yes, gives 7, solved it. This isn't even worth trying to look for a more analytical solution.
- OscarCunningham 11y agoBut since I didn't know in advance that the solution would be one of the smaller possible answers it was faster in expectation to solve the problem using the given method.
- tromp 11y agoThe question at the actual competition was slightly more subtle: it asked for m modulo 10. So it would have taken rather more tries to find 18...
- laxatives 11y agoMartin Gardner has a bunch of books with short brain teasers of various levels of complexity. Most of them are like $2 on Amazon.
- octonion 11y agoSmallest positive m such that 77 divides m^2+7m+89 is greatly simplified by realizing (mod 77) m^2+7m+89=m^2+7m+12=(m+3)(m+4).
- baddox 11y agoThat's precisely how the article explains it.
- imaginenore 11y agoRead the article.
- vanattab 11y ago<nitpick> m^2+7m+89 != m^2+7m+12 (m^2+7m+89)%77 =(m^2+7m+12)%77 </nitpick>
- Hermel 11y agoAnd how does the ability to solve these puzzles make you a good quant?
- baconizer 11y agobecause it takes years of training/experience/luck/success to be invited sitting to solve them while sipping champagne on the house. :)
- officialchicken 11y agoBut what if you prefer qualitative? Can you out-smart Warren Buffet [1]? [1] http://www.forbes.com/sites/investor/2011/10/11/warren-buffetts-investing-formula-revealed/ http://www.forbes.com/sites/investor/2011/10/11/warren-buffe...
- eru 11y agoWarren Buffet does lots of quantitative reasoning as well: on balance sheets rather than fluctuation of market prices.
- random_coder 11y agoFor 5), 89 modulo 77 is 12 so we just solve for the least m such that (m + 3) * (m + 4) (= mm + 7m + 12) is divisible by 77. Both 73 and 74 clearly satisfy the condition, but 18 + 3 = 21 divisible by 7 and 18 + 4 = 22 divisible by 11 is the least among the choices.
- theoh 11y agoMaybe there's a subtle irony to reflect on here - which is that intelligence is something diverse and qualitative, not just a single quantitative scale from dumb to smart.
- vinchuco 11y agoThe way I heard it last time was that intelligence is like running a race to get to a place (the solution to a problem). It doesn't matter how fast you run if you're going the wrong direction.
- eachro 11y agoSomehow I'm sure that some of the other problems must be a lot harder. Why else would heavy hitters like Poh Shen Lo and other past IMO competitors bother with this?
- ipince 11y agoBecause it's for charity.
- newman314 11y agoI have to admit the factoring threw me for a bit. The last time I had to do something like this was over 20(!) years ago. Although it was gratifying to have the solution drift into mind after a while. What is sad is that I'm acutely aware that I no longer think as quickly as I did in my 20s.
- idontgetit_ 11y agoWhat's annoying me about the second question is the distinction I'm thinking about what constitutes a handshake: are we determining that the number of hand shakes - grasping of the hands between two people constitutes a handshake; or - the number of times one moves their hands up and down is the hand shake so I'm thinking the former, but still finding it difficult to see how the number of handshakes can ever be odd. You need at least two people, the sum of their hand shakes is even, you add a third, and everyone shakes hands at least once, so the sum of all their handshakes is even. I'm not sure the rest of the solution can involve any odd numbers. i have a mental hurdle -- i'm not thinking about it in the right way
- maxander 11y agoIf there's only two teachers at the convention and they shake hands, that's just one handshake- an odd number. The count is an "objective" count of all handshake-events, not the sum of everyone's personal handshake counts. Writing unambiguous math problems is a surprisingly hard thing to do!
- mrcactu5 11y agoVery surprised to see Manjul at one of the tables