i have a problem with this maths question:
How many squares are on a chess board, including 2 x 2 squares etc. can anyone help??????
i have a problem with this maths question:
How many squares are on a chess board, including 2 x 2 squares etc. can anyone help??????
Try counting them.
Code:#include <cmath> #include <complex> bool euler_flip(bool value) { return std::pow ( std::complex<float>(std::exp(1.0)), std::complex<float>(0, 1) * std::complex<float>(std::atan(1.0) *(1 << (value + 2))) ).real() < 0; }
1x1 squares : 8x8 =64
2x2 squares : 8x8 - 15 = 49
3x3 squares : 8x8 - 15 - 13 = 36
...
8x8 squares : 8x8 - 15 - 13 - ... = 1
The number os positions for 1x1 squares is 64
All but 15 positions can hold the top-left corner of a 2x2 square etc.
To advertise a bit i wrote a simple program in Omicron to calculate the number of squares:
Just run it using the online compilerCode:order = 8 squares = 0 repeat squares += 8*8 - (-order^2 + 18order - 17) until (order-=1)==0 print squares
I case you're in a hurry, the answer is 204.
Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling
So why didn't you write it in C? After all, this is a C-board .
MagosX.com
Give a man a fish and you feed him for a day.
Teach a man to fish and you feed him for a lifetime.
Hehe, but this is General Discussions.
And C++ requires main() and #includes
Anyway, this should satisfy everyone:
Code:#include <iostream> main() { int order = 8; int squares = 0; do { squares += 8*8 - (-(order*order) + 18*order - 17); } while (--order != 0) std::cout << squares; }
Last edited by Sang-drax; 10-20-2002 at 07:49 AM.
Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling
Sorry, SangDrax, but your function will only count the number of 8x8 squares (which is 1) thanx to your while condition .
Anyway, if you want an even simplier function to calculate it, here:
(Output: 204)Code:#include <iostream.h> #include <conio.h> int Count() { int Squares = 0; for(int i=1; i<=8; i++) { Squares += (i * i); } return Squares; } int main() { cout << "Nr of squares: " << Count() << endl; getch(); return 0; }
Oops! It's been corrected.Originally posted by Magos
Sorry, SangDrax, but your function will only count the number of 8x8 squares (which is 1)
Hehe, you're right that there is a simpler algorithm.
I didn't think that much, just generated a formula for the sequence I wrote above.
Now that I've thought a little, I have an even simpler solution:
(faster for large n, at least)
where n is the width of the boardCode:squares = (2n^3 + 3n^2 + n) / 6
Last edited by Sang-drax; 10-20-2002 at 08:40 AM.
Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling
Eh, n shouldn't be the number of squares, it should be the width of the board (8 in a chess board) .
n=64 gives 89440.
What did you use to get that formula. It doesn't look like the formula for a geometric sum.
MagosX.com
Give a man a fish and you feed him for a day.
Teach a man to fish and you feed him for a lifetime.
Sorry for the typo once again
The formula can be proved using induction:
Assume that it is correct for n=k, then use that assumption to prove that it must be true for n=k+1.
Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling
AhhOriginally posted by Magos
What did you use to get that formula.
I used my program "Sequence finder".
I've attached it here.
If you want the source, download Omicron.
Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling