Does the set {1;2;...;3000} contain a subset A consisting of 2000 numbers
such that x belongs to A implies 2x does not belong to A.
9hmm b555 tell me do u have the solution for this ?
i donno how u accepted nishant sirs solution !
oopsy sir u dint see 3,6 sitting together ?
9urs ofc
dude b4 this u were postin much tuffer Qs
so no one had time to solve it
9note :
#9 method to find the summation shud read as [3000/r.4Sr]
its inelegant
see below
another way for S1 + S2 + ......
6 X ( no of odds < 3000/1024)
+
5X(no of odds <3000/256 - odds<3000/256)
+
....
...
= noof odds <3000/1024 +odds <3000/256 + ..... + odds<3000
= 1+6+23+94+375+1500 = 1999 !
39hope everything is cleared now.
and thanks for pointing out celestine !!
39Consider 1001 nonoverlapping pairs of form (a,2a)
1500,3000
1499,2998
...
751,1502
375,750
...
188,376
93,186
...
47,94
23,46
...
12,24
5,10
4,8
3,6
1,2
There are 998 numbers from {1,...,3000} which is not in pairs ==> for any 2000 numbers no less then 1002 lay in pairs ==> two numbers in the same pair
62oh yeah i got excited too fast :P
i thought i did solve another bhargav toughie :P
but not to be...
See the new set of numbers
39wait , wait , wait
yes even i missed 3,6.
you are right.
wait i am working on it right now
62Lets take the numbers from 1501 to 3000
then from 376 to 750
then from 94 to 187
then from 24 to 46
then from 6 to 11
then from 1
1500+375+94+23+6+2 = 1999
Proved by construction of the set that this is possible. :)
Mistake pointed out by celestine
9sir how does 3 and 6 both come !
ans is most probably impossible
method of working
let r be odd <3000
now there are no issues in including that in A
now u find that u can always get max no in set A if u include r,4r,16r,64r,256r,1024r whenever feasible ( can u see why ? )
now come to the evens any even of form 2r,8r,32r,128r,512r,2048r with r odd neednt be included from above reasoning
so our nos are
S1 + S3 + S5 +... Sr +S2999
where Sr is minimum value for [ 2000/r.4Sr ] = 0
62:D
yeah I am trying to spednd sometime here again..
life's suddenly become very busy.. there has been a lot of work..
And unfortunately i have become a bit money oriented... (I have to earn someday :P)
39ya anyways fabulous work.
AND HAPPY TO HAVE U BACK NISHANT `SIR` [58]
39not air lightning sir , but your genious awakened
( i dont mean it always keeps sleeping :D)
62First i got lost in all the pigeon hole arguements and god knows what all...
Then from the air lightning struck me and i got the solution :D
341fantastic!! :D
edit: admiration expressed w/o proper investigation :D