Problems, and other interesting diversions !
I'm planning to start a problem-solving club along with a few of my friends in this lab. We will pick some interesting mathematical and logic problems and discuss them once a week. I'm hoping this will help us stay ( or become:-) mentally sharp :-) I've always loved maths, but over the years, I've changed my gears from one where I was in a quest for understanding complexity to one where I'm in search of elegance.
So, we will pick problems that involve simple ideas, but which need a good deal of ingenuity so solve. In math, there are a remarkable number of non-trivial results that can be arrived at by clever application of elementary ideas. I can think of a couple of results offhand that seem extremely hard to prove, but which can in fact, be solved very elegantly using some simple concepts -
1) Prove that there are an infinite number of primes.
2) For every number 'm', prove that there exists a number 'n', such that the product of the two, m*n is a number that contains only ones and zeros .
Interesting, both these have solutions that someone in high school can probably understand ! There is also a class of logic puzzles I stumbled upon a few years ago that involves a touch of psychology !:-) I'm looking forward to discusssing some of them with these guys. At this point, I'm reminded of an interesting quote - 'There are three kinds of mathematicians- those who can count, and those who cannot' !:-) Let's see which category we end up falling into !
I'm planning to start a problem-solving club along with a few of my friends in this lab. We will pick some interesting mathematical and logic problems and discuss them once a week. I'm hoping this will help us stay ( or become:-) mentally sharp :-) I've always loved maths, but over the years, I've changed my gears from one where I was in a quest for understanding complexity to one where I'm in search of elegance.
So, we will pick problems that involve simple ideas, but which need a good deal of ingenuity so solve. In math, there are a remarkable number of non-trivial results that can be arrived at by clever application of elementary ideas. I can think of a couple of results offhand that seem extremely hard to prove, but which can in fact, be solved very elegantly using some simple concepts -
1) Prove that there are an infinite number of primes.
2) For every number 'm', prove that there exists a number 'n', such that the product of the two, m*n is a number that contains only ones and zeros .
Interesting, both these have solutions that someone in high school can probably understand ! There is also a class of logic puzzles I stumbled upon a few years ago that involves a touch of psychology !:-) I'm looking forward to discusssing some of them with these guys. At this point, I'm reminded of an interesting quote - 'There are three kinds of mathematicians- those who can count, and those who cannot' !:-) Let's see which category we end up falling into !
8 comments:
Karthik, please do share the problems here (along with the solutions for some of us mathematically-challenged ones!). I would love to figure out the logic puzzles too :). Great initiative!
Neeraja, Ya sure ! If you are interested, I can put up some of them here. Those that involve figures will be hard for me to transcribe, but the rest I can :-)
As we know, we've infinite number of numbers. And just within 1 and 10 we have 4 prime numbers! Hmm, logically makes me believe there are infinite primes :D Of course thats no proof. Hmm, now I already need to give my brain a little rest, so I'll think about that m*n a little bit later :D
Anonymous - Yes, thats a good intuitive start! Though I suspect the average spacing between the primes increases. ha ha, ya you can think about it later:-)
Awesome. :) You should and must post the problems. Do you have any other chapters of this club?
Rafiki - What chapters ?! So far, with some difficulty, I've convinced 2-3 guys :-) Hpoefully, there wil be 5 of us in the end! So, chapters and all is far off !:-) If people don't turn up, I'm planning to solve some anyway :-)
You should start an online community. This will help break the barriers of time and distance. I am sure there will be more than 5 people interested then.
Not too long ago there was a puzzles community on orkut(RIP Orkut) which was really active and doing what it promised (pose and solve puzzles). This reminds me of that. A few friends and I would take a puzzle a week and (try to)solve them. Sweet memories. :)
Rafiki - Online community would be good, but i feel puzzles are easier to discuss in person, since you can explain an idea by writing down an equation or drawing a figure. That's hard to do in this form ! Anyway, I think I'll start one and we'll see how it goes !:-)
Post a Comment