Hmm, maybe I'm not looking at the right board. I just counted on the one closest to me. Does your chess board look like this?
I still count seven. How many do you see if you're so sure I'm wrong?
What is the total number of squares on chessboard?
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Ok, here I marked them.
Damn I forgot to carry the 3.
Yeah, the 3rd one was the hardest to find.
Jul 12, 2013
0
#26
I'm inclined to believe anyone who displays such deft, free-hand mouse work.
Equations and calculations? Balderdash and fiddle-faddle!
Lol im stupid... obviosly (1+2+3+4+5+6+7+8)^2 works....
waffllemaster wrote:
Yeah, the 3rd one was the hardest to find.
haha, excellent.
cjt33 wrote:
Lol im stupid... obviosly (1+2+3+4+5+6+7+8)^2 works....
The number of squares on an nxn board seems obvious with just 1^2 + 2^2 + . . . + n^2
But the number of rectangles on an 8x8 board being (1+2+3+4+5+6+7+8)^2 isn't obvious... at least to me. Curiously it's also 1^3 + 2^3 + . . . + 8^3.
TenyVarona wrote:
@cjt33: There is a much simpler way to do this. Just follow this formula:
Number of rectangles (nxn board) = [n(n+1)/2]^2 = [8*(9)/2]^2 = 36^2 =1296.
I think, you will now agree that this is very easy! Lol!
no it is just that the equation [n(n+1)/2]^2 is exactly the same as (1+2+3+4+5+6+7+8)^2
Also,
1 + 2^3 + 3^3 + ... + (n-1)^3 + n^3 = [ 1 + 2 + 3 + ... + (n-1) + n ]^2
= [n(n+1)/2]^2
You can derive the formula if you want... but, leave it to math or engineering students. Lol!
or 13 year olds like me =)
Lol! at your age, you still have a lot of things to learn. Unless you are genius, you cannot derive the formula for this problem.
Okay, okay, here's one:
Think of the way a Knight moves (Bob Seger is heard in the background). Say it's all by itself on the chessboard, at a1. It can move from there to b3 or c2. If it were at a2, it could move to c1, c3, or or b4. If it were at a3, it could move to b1, c2, c4, or b5. I hope you're catching on. So the question becomes:
What is the total of the available destinations for a Knight played from each of the 64 squares?
I've got the answer. If someone comes up with a formula like they did for the number of squares and rectangles on a chessboard, I'll be really impressed.
I think I actually figured this out once... but I can't remember what the question was and I can't remember what this is the answer to... all I have written by knight is the number 336. I have a number for each piece lol.
Is this the answer? I'm curious what 336 has to do with the knight and this may be it.
Man I thought memorizing the Knights Tour was enough. Now this takes chess obsession to a whole other level.
corners 2 squares
rim 3 squares
2nd/7th ranks b/g files 4 squares
3-6th ranks c-f files 8 squares
4x2=8 3x24=72 (80) 20x4=80 (160) 16x8=128 (288)
288 available moves yet only 64 squares.
coneheadzombie wrote:
Unless you mean something else which you probably do
I think he means a1 + b1 + c1 would equate to 2 + 3 + 4
A central square would have 8. I think he makes the distinction for to and from so while a1 has 2 possible moves b3 would still have 6 even after counting a1.
There are a total of seven sqaures on a chess board. Double check me on this though.