Chess is a recreational and competitive game for two players. It is derived from Persian Shah ("the King"), an abbreviation of Shâh-mât (Checkmate).wikipedia
Today, chess is one of the world's most popular games, played by millions of people worldwide2.Playing chess is really cool! It helps you develop your mind, patience, courage and perseverance! It will train you how to have a good decision making, to sacrifice for the benefit of the majority, and to achieve your goal diligently! I know you are one of them! Right?
But did you realize how many squares are there on a chessboard? Yes, we've been playing a lot of times but we didn't even ask the exact number of squares on it!
So what are you waiting for? Find how many squares are there on a chessboard? Give your brief explanation how did you get it supported by formulas to make sure that you are not cheating!!!
Renz Reyes!
You made it!
Your explanation is accepted but if you could give the formula you will be on the Second Level!!!
Friday, November 30, 2007
Are you Checkmate?!
Posted by percival at 5:27 PM
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1x1 boxes = 64
2x2 boxes = 49
3x3 boxes = 36
4x4 boxes = 25
5x5 boxes = 16
6x6 boxes = 9
7x7 boxes = 4
8x8 box = 1
total: 64+49+36+25+16+9+4+1 = 204
how did you get this...can you send me the formula he he he
my answer is 204 boxes....the formula???? well i don't have an accur8 one but i guess i'll give it a try. from the info i made from this problem, my formula would have to be the number of squares you can count in a row raise to the power of 2, with regards to their size. example, 1 x 1 boxes=8 boxes in a row, then 8 raise to 2=64. so you already have 64 boxes, then 2 x 2 boxes=7 boxes in a row then 7 raise to 2 = 49. then just do the same with the other boxes until you get the largest box possible then add them. mine is 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2 = 204.
i didn't have a formula-- unlike renz who had one. i counted it manually. i took a chess board and then counted the boxes. haha!!!
first i counted with the smallest size.. then down to the largest square which was 8x8 boxes. as simple as that. =)
renz you got the exact number of squares and your formula is quite right! Congratulations! You made it but if you could give me the simpliest and easiest way (formula) to get the exact number of squares you will be on the second level!!! Keep up the good work!!! You can challenge the brightest student in math or even your teacher!!!
Percy,
Keep up the the good work. Sooner or later I will join to contribute some solving problem which is also very educational and ineteresting. I have a lot in my "Baul" to share in this blog.
Renz, I am very proud of you my dearest son. Kudos to you.
there is a formula for the sum of the square numbers and that for mula is n(n+1)(2n+1)/6.
so if you have 8x8 square grid, to get the total number of squares, just substitute 8 in the formula.
the explanation of renz is correct. actually, if you have an 8x8 grid, just work with one row. to get the number of1x1 small square just count the number of 1x1 in the first row and square it. to get the number of 2x2 square, get the number of two 1x1 (pair) in the same row and square it. now why are we squaring those numbers? it's because since we are working with square, the number of squares horizontally is equal to the number of squares vertically. oks na ba yan? -jinky :)
yeah yeah - but does ANYONE know how to GET the formula - I don't know how to arrive at it!?
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