Well What do you mean by a good problem ?
It is the one whose solution should not require any prerequisites except cleverness. A high school student should not be disadvantaged compared to a professional mathematician. Yes, With problems requiring cleverness only with check the mind of the person only not by learning and knowing the whole thing.
Well I came across such a problem last night and here it is for all of you.
Problem. In a Finite sequence of real numbers, every 7-sum is negative, whereas every 11-sum is positive. Find the greatest number of terms in such a sequence.
Well The above was an IMO problem of 1977 and it was a problem for 6 points only. It requires nothing but a common sense generating from inside. It is not different for a 10th standard student and not for a professor.
Well Try it And do comment your responses.
common sense ki kami malum hoti hai, kaafi dino se dekh rha hun, no replies!
ReplyDeletecan u please give some idea how to start?
better explain the question first! :D
ReplyDeleteWell Akash bhaiya.. You are Right !!
ReplyDeleteMujhe Laga nahi tha ki iss problem pe itna time lagega..
The only hint jo iske solution se aa rhi hai ki you have to use ubiquitous extremal principle
well The extremal Principle tells us to pick an object which maximizes or minimizes some function. The Resulting object is then shown to have the desired property by showing that a slight variation would further increase or decreasethe given function. It is constructive giving an algorithm for constructing the object..
See if something happens with this.. nahi toh i will post the solution soon !
I will see! dont post the solution soon !
ReplyDeleteWell Its Ok as you say bhaiya.. :D
ReplyDeleteBt bhaiya sach mein this question is pure common sense !! Doesnt requires any mathematical prerequisites !! sach mein.. normal life ki tarah socho !!
main konsa E=mc^2 soch raha hun!
ReplyDeletekabhi kabhi strike nahi karta, kal HRT hai, dimag ghum rha hai vese hi :D
Well Best of luck for the HRT bhaiya..
ReplyDeleteits alright.. kounsa har kissi ko strike karta hai ? :D
Do well in HRt as you alwys do :D
heyy... devansh u should have first defined n-sum... anyways... here is a simple approach to this question....let the numbers be a1 a2 ...
ReplyDeletewe make a table like this...
a1 a2 a3 a4 a5 a6 a7
a2 a3 a4 a5 a6 a7 a8
a3 a4 a5 a6 a7 a8 a9
....
....
a11 a12 a13 a14 a15 a16 a17
now
see
sum of all rows is -ve... and all columns is +ve...
so
we have net sum of matrix..both positive and negative... contradiction!!!
so
max 16 terms...
Saale Good.. you are absolutely right singhal ;)
ReplyDeleteI was thinking to post it today but jab tak tu zinda hai tab tak tension ki baat hi nahi :P :D