Fun little math problem

05112016, 09:23 AM
Post: #21




RE: Fun little math problem  
05112016, 10:43 AM
Post: #22




RE: Fun little math problem
Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05112016, 11:37 AM
(This post was last modified: 05112016 11:40 AM by Gerson W. Barbosa.)
Post: #23




RE: Fun little math problem
(05112016 07:57 AM)Paul Dale Wrote:(05112016 06:31 AM)Dieter Wrote: How did you do it? It looks like you and Dieter have tackled the problem the same way it was done more than one hundred years ago by young Ramanujan: "One afternoon back in 1902, during recess, an older student, said to be the smartest in his class, handed him a math problem. Ramanujan was so smart? Well, then, let him solve this: At first glance falling under the familiar heading of “two simultaneous equations in two unknowns,” the problem actually confronted Ramanujan with a difficult fourthdegree equation and meant recalling a theorem applicable to a particular class of them. To any ordinarily smart fourteenyearold, it would be exceedingly difficult. “To my astonishment,” Rajagopalachari remembered later, “Ramanujan worked it out in half a minute and arrived at the answer by two steps.” In fact, he probably didn’t “work it out” at all, but simply looked at it, guessed the answer might be one where each was a square, tried a couple of possibilities in his head, and saw the solution, x = 9 and y = 4, jump out at him; in other words, it was a piece of fancy footwork, nothing mathematically profound." From "The Man Who Knew Infinity: A Life of the Genius Ramanujan (English Edition)" by Robert Kanigel. 

05112016, 01:07 PM
Post: #24




RE: Fun little math problem
(05112016 07:57 AM)Paul Dale Wrote:(05112016 06:31 AM)Dieter Wrote: How did you do it? I had a similar path, slightly different though. From both equations I figured both x and y had to be perfect squares. Then looked at the first equation and y had to be less than 7, which left me with 4 as the only answer, leading to sqrt(x)=3. Visually tested the 2nd equation and turns out it worked. 

05112016, 02:23 PM
Post: #25




RE: Fun little math problem
(05112016 11:37 AM)Gerson W. Barbosa Wrote:(05112016 07:57 AM)Paul Dale Wrote: I figured the missing values were integers & it was then clear that they must be small. There were not a lot of options left: 2 & 4, 3 & 9, 4 & 16. I got it right first go after this. Amazing: I didn't imagine it could be so difficult to see the solution. My previous comments stem from me doing almost the same, in a similar amount of time. And my brain is four times older than Ramanujan's. I only wish I could have a glance to the other 99999 things he saw that I am still blind to... Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05112016, 05:13 PM
Post: #26




RE: Fun little math problem
(05112016 02:23 PM)Massimo Gnerucci Wrote: Amazing: I didn't imagine it could be so difficult to see the solution. My previous comments stem from me doing almost the same, in a similar amount of time. And my brain is four times older than Ramanujan's. Quite easy indeed. So let's be mean, but not so mean: :) \(\left \{ _{\sqrt{y}+x=4}^{\sqrt{x}+y=2} \right.\) No numerical solutions, please. 

05112016, 05:24 PM
(This post was last modified: 05112016 05:28 PM by Massimo Gnerucci.)
Post: #27




RE: Fun little math problem
(05112016 05:13 PM)Gerson W. Barbosa Wrote:(05112016 02:23 PM)Massimo Gnerucci Wrote: Amazing: I didn't imagine it could be so difficult to see the solution. My previous comments stem from me doing almost the same, in a similar amount of time. And my brain is four times older than Ramanujan's. Zerofour? :D Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05112016, 05:26 PM
Post: #28




RE: Fun little math problem  
05112016, 05:28 PM
Post: #29




RE: Fun little math problem  
05112016, 05:30 PM
Post: #30




RE: Fun little math problem
(05112016 05:28 PM)Dieter Wrote:(05112016 05:24 PM)Massimo Gnerucci Wrote: Zerofour? :D Too easy if you don't mix up... ;) Greetings, Massimo +×÷ ↔ left is right and right is wrong 

05112016, 06:14 PM
Post: #31




RE: Fun little math problem
(05112016 05:26 PM)Dieter Wrote:(05112016 05:13 PM)Gerson W. Barbosa Wrote: Quite easy indeed. So let's be mean, but not so mean: :) Oops! I'd make for a good math teacher (for students). Kind of those who don't know how to set up a problem :) Ok, let's try again: Find both solutions to \(\left \{ _{\sqrt{y}+x=4}^{\sqrt{x}+y=2} \right.\) Closedform solutions only. 

05112016, 06:17 PM
(This post was last modified: 05112016 06:18 PM by Gerson W. Barbosa.)
Post: #32




RE: Fun little math problem  
05112016, 06:38 PM
Post: #33




RE: Fun little math problem
(05112016 05:13 PM)Gerson W. Barbosa Wrote:I could reduce the problem to a 3rd degree equation and solved it with Wolfram.(05112016 02:23 PM)Massimo Gnerucci Wrote: Amazing: I didn't imagine it could be so difficult to see the solution. My previous comments stem from me doing almost the same, in a similar amount of time. And my brain is four times older than Ramanujan's. Result is huge... 

05112016, 07:29 PM
Post: #34




RE: Fun little math problem
(05112016 06:38 PM)Tugdual Wrote:(05112016 05:13 PM)Gerson W. Barbosa Wrote: Quite easy indeed. So let's be mean, but not so mean: :)I could reduce the problem to a 3rd degree equation and solved it with Wolfram. That's what math softwares are for :) There was a time when these were done by hand, but I don't think this makes sense today. Most important thing is that you know what you're doing and leave the hard work for the machine. 

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