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The only important squares is the 64 that you play with.
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.
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.
And trying to make some fromt page drive in news.
Working on our KNIGHT MOVES
You're forgetting the sqaures that only have 6 possible moves!
So instead of 3x24 I think you should have 8x24, the other 16 sqaures have 6 possible moves.
So 4x2 + 8x3 + 20x4 + 16x8 + 16x6 = 336
I guess that solves my mystery :p
Here's the old picture I have on my computer:
you're forgetting to include (for the extra fun) checks, checkmates and captures and the different notations that arise when two (or more!) knights can jump to the same square *head spins*
Congrats! You were first, wafflemaster! 336 it is!
Strange how the Knight moves ...
Why are we even talking about this?
Because intelligent creative people are like that. Curious minds, trying to solve problems, investigate, observe, analyze. People probably said the same thing about trig and calculus until masterpieces of engineering occured as a result of their power. It was nerds scoping out mathematical relationships that developed some of the best tools mankind has.
I can only be SO obsessed, heinzie! Maybe you can handle that one ;-)
Yeah! What he said :-P !
How about 68 squares? My friends and me tried a variation with standard board plus 4 "virtual squares", d0-e0-d9 and e9! We added 2 grasshoppers and 2 nightriders as fairy pieces. White grasshopper starts at d0 (behind the white queen), white nightrider starts at e0 (behind the white king), black grasshopper starts at d9 (behind the black queen and the black nightrider starts at e9 (behind the black king). It's only virtual square, once leaving its starting square the piece can't return back on it. A wild game and almost new one!!! Grasshopper is like a minor piece but the nightrider is a very strong one, almost as strong than the queen. Something to try...
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.
Ok... I guess I will take that as a compliment... Its actually not that hard to be good at math you know. These things just come eisily to me...
Assuming squares can overlap, then = 204
I did not yet think about rectangles but it is very interesting question!
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