official quant thread for cat08

[eric.segal1]

On a chessboard of 64 small squares. In how many ways can u select two squares of the same dimension such that they have a common side?
168
228
288
348
114


puys m getting 248 as my answer. plz help me out with this problem.

ps: plz provide adequate explanation.

[eric.segal1]

the answer given is 228

[eric.segal1]

Originally Posted by Wynand

This qs has been posted before. So sorry to break the flow of this thread, but I will really appreciate it if you could provide help again. There is obviously a big hole in my concept

The no of integral solns of |x| + |y| <= 4

My soln -> As mod of x = x when x>0, and -x when x<0.
So |x| + |y|<=4 in the 1st quadrant (x>0,y>0) will have 15 solns
In the 2nd quadrant (x<0,y>0) it becomes -x+y<=4, which shall have infitnite solns as
y-x can be <=4 for infinite sets of (x,y) values .

The incumbent Quant Gods went about it calculating the solns in 1st quadrant as 15, abd in 4 quads as 15 x 4 = 60. And subtracting values common to all quadrants like (x=0,y=0) and axis points, arrived at 41.

Please Help!

a good way to solve is following

each quadrant has 4+3+2+1=10 integers(leaving one axis and origin every time)
now mlutiply it by 4(coz there r 4 axes) = 40
while doing this u have counted all the axes integral points except the origin.
so add the origin 40+1=41
hence the answer


ps : this method is better understood when visualised graphically

[manas_cat2008]

Originally Posted by eric.segal1

Originally Posted by eric.segal1 (mind blowing concepts@quant)
On a chessboard of 64 small squares. In how many ways can u select two squares of the same dimension such that they have a common side?
168
228
288
348
114


puys m getting 248 as my answer. plz help me out with this problem.

ps: plz provide adequate explanation.

hi Eric...good question to start...btw if interested in combined prep let me know...u can let me know

http://www.orkut.com/Profile.aspx?ui...10067777942530

[eric.segal1]

Originally Posted by manas_cat2008

hi Eric...good question to start...btw if interested in combined prep let me know...u can let me know

http://www.orkut.com/Profile.aspx?ui...10067777942530

ok dood m interested.

[SUPER XERO]

<space reserved for solution>

[eric.segal1]

Originally Posted by SUPER XERO

<space reserved for solution>

ok dood its good to know that someone got it

[SUPER XERO]

dude..... making the diagramm ...... will post the solution asap.......

[nbangalorekar]

Originally Posted by SUPER XERO

hey........ can u explain how you would use PnC to solve this question????

suppose u have 'n' different variables. consider different cases like only one variable is zero, two of the variables r 0, and so on upto (n-1) varibles zero.
for the remaining variables use partition formula (n-1Cr-1) n multiply it with 2^m wher m is the number of variables u r considering for that case.
this method is better since u can use it for ne number of variables....

[stalwart_itsme]

Originally Posted by eric.segal1

On a chessboard of 64 small squares. In how many ways can u select two squares of the same dimension such that they have a common side?
168
228
288
348
114


puys m getting 248 as my answer. plz help me out with this problem.

ps: plz provide adequate explanation.

Each square has got 4 sides. Totally 64 squares. 32 blacks and 32 whites. so total number of sides is 32(black/white)*4=128. We are taking only 32, as we are eliminating the sides being repeated.

Now each side has two squares in common, so total ways in which squares can be selected 128*2=256.

The squares on the edges of chess board has one side which is connected with only one square,that is the side which forms the edge of the chess board. so eliminating those sides, which is 28 of them, we get 256-28=228

I hope explaination is correct...!!!!