Puzzle: Numbers on BlackBoard

[khanna_sumit]

Originally Posted by Eccentric

very well done sumit!

The original state of the system is:
{even, even, odd} i.e.the number of 1's, 2's and 3's resp.
Any operation toogles the state of each 3 parameters.
Hence, the final state of the system will be either of {odd, odd, even} or {even, even ,ood}.
If only one number remain this corres. to set {even,evn,odd) i.e. {0,0,1} a 3 remaining on the board.
Again if you play judiciously, this final state can always be achieved unless we start with number of only one type(i.e just 3's or 2's or 1's).

We can also put a count check, i.e. in start we have 85 numbers,each operation reduces that by 1 and after 84 operations we will have 1 number reamining on board and the same state we started with {even,even,odd}.

Had we started with {odd,odd,even} we would have obtatined same results.
This also goes on to show that if we start with {odd, odd, odd} or {even,even,even} we can't end up with just one number it will either be 1 number of each type or finally 2 numbers of any type

hi eccentric,

i liked ur idea of posting fresh problem on a new thread.....or we may lose track of the discussion.......specially if a person joins late, he may become confused...and an appeal to the pagalguy.com people should be made to introduce some diagramming tools in the quant discussion threads..........im going to post a new problem on a new thread.......lets discuss it..........

[Eccentric]

Originally Posted by khanna_sumit

hi eccentric,

i liked ur idea of posting fresh problem on a new thread.....or we may lose track of the discussion.......specially if a person joins late, he may become confused...and an appeal to the pagalguy.com people should be made to introduce some diagramming tools in the quant discussion threads..........im going to post a new problem on a new thread.......lets discuss it..........

for image hosting upload image on the following link
http://www.imageshack.ws/
you get a link to upload right on this page only...



Then this page will provide you a couple of Hotlinks for forums and a direct link....
you can paste the hotlink and image will be displayed .. the same I used for TetraHydron!

[Govi]

Originally Posted by Eccentric

very well done sumit!

The original state of the system is:
{even, even, odd} i.e.the number of 1's, 2's and 3's resp.
Any operation toogles the state of each 3 parameters.
Hence, the final state of the system will be either of {odd, odd, even} or {even, even ,ood}.
If only one number remain this corres. to set {even,evn,odd) i.e. {0,0,1} a 3 remaining on the board.
Again if you play judiciously, this final state can always be achieved unless we start with number of only one type(i.e just 3's or 2's or 1's).

We can also put a count check, i.e. in start we have 85 numbers,each operation reduces that by 1 and after 84 operations we will have 1 number reamining on board and the same state we started with {even,even,odd}.

Had we started with {odd,odd,even} we would have obtatined same results.
This also goes on to show that if we start with {odd, odd, odd} or {even,even,even} we can't end up with just one number it will either be 1 number of each type or finally 2 numbers of any type

Hey Eccentric

If I am not wrong I think this problem is from the MINDSPORT Column by Mukul Sharma which comes in The Sunday Times.

Is it???

Regards

Govi...........

[Eccentric]

Originally Posted by Govi

Hey Eccentric

If I am not wrong I think this problem is from the MINDSPORT Column by Mukul Sharma which comes in The Sunday Times.

Is it???

Regards

Govi...........

moi duuno
I pick it from Orkut Puzzle community.

[Govi]

Originally Posted by Eccentric

moi duuno
I pick it from Orkut Puzzle community.

Yup buddy

I checked it. Its from this column on MindSport.

I think we could turn this thread into a discussion for such problems it would be great. Well some of the problems are beyond the domain of what is needed in competitive exams but still they are based on very strong fundas.

Cheers

Govi...........

[theshikha]

My first post!

this thread and similar ones are great.. Thanx Eccentric DesiGuru, Govi, Gaurav for valuable insights!

Keeping in with the tradition I am posting this weeks one!

A man is walking down a street along which runs a tram line. He notices that for every 40 trams which pass him travelling in the same direction as he, 60 pass in the opposite direction. If the man's walking speed is three miles per hour, what is the average speed of the trams? (Doen't it looks like CAT'05 2 mark question! )

Though i have an answer but the approach was clumsy. Lets see waht other people has to about it.

[Eccentric]

Originally Posted by theshikha

My first post!

this thread and similar ones are great.. Thanx Eccentric DesiGuru, Govi, Gaurav for valuable insights!

Keeping in with the tradition I am posting this weeks one!

A man is walking down a street along which runs a tram line. He notices that for every 40 trams which pass him travelling in the same direction as he, 60 pass in the opposite direction. If the man's walking speed is three miles per hour, what is the average speed of the trams? (Doen't it looks like CAT'05 2 mark question! )

Though i have an answer but the approach was clumsy. Lets see waht other people has to about it.

Visualization helps..
Lets say the man was stationart standing in he middle of long track, a lot of trams on the tracs passing him in both direction. Say the speed of tram is A.
Considering that trams are passing him regularly so trams are equispaced (at equal distance from ech other on tract).
If the man starts walking towards one side lets change the velocity of trams to relative velocity and again assume man to be stationary. Just the trams going to one direction got faster and the other got slower.. ! As the ditance between trams is still equal just the velocity has changed, the number of tarams passing him is directly proportional to speed:

(A + Speed(man)) / (A - Speed(man)) = 60/40 = 18/12 = 15+3 / 15 -3
So speed of tram = 15 kmph

[khanna_sumit]

Originally Posted by theshikha

My first post!

this thread and similar ones are great.. Thanx Eccentric DesiGuru, Govi, Gaurav for valuable insights!

Keeping in with the tradition I am posting this weeks one!

A man is walking down a street along which runs a tram line. He notices that for every 40 trams which pass him travelling in the same direction as he, 60 pass in the opposite direction. If the man's walking speed is three miles per hour, what is the average speed of the trams? (Doen't it looks like CAT'05 2 mark question! )

Though i have an answer but the approach was clumsy. Lets see waht other people has to about it.

ratio of relative speeds of the trams running in same and opposite direction will be 60:40.....i.e. 3:2.........if we assume that speed of the tram is x miles/hr..then relative speeds are x-3 and x+3....and their ratio is 3:2.....therefore x+3/x-3=3/2....solving it we get.....x=15........

[reachmonil]

Originally Posted by theshikha

A man is walking down a street along which runs a tram line. He notices that for every 40 trams which pass him travelling in the same direction as he, 60 pass in the opposite direction. If the man's walking speed is three miles per hour, what is the average speed of the trams? (Doen't it looks like CAT'05 2 mark question! )

Hie shikha...

first the pleasantaries... welcome to the bandwagoN!!

okies.... firstly.... i solved it sum wierd way... dunno a bit if i m correct or no... just sum mental calcs ..... is the answer 15miles/hr!?

[reachmonil]

hey...

summit n eccentric bhai.... by the time i looked at shikha's post... n was replying... i c u both have already posted the soln... n all bng on target!! PG rocks ! will be fun preparing together for CAT05! wats say!?!