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---- Nous avons besoin d'un traduction français!
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204 squares on a chessboard.
(8**2)+(7**2)+(6**2)+(5**2)+(4**2)+(3**2)+(2**2)+(1**2) -or- 64+49+36+25+16+9+4+1
At first I thought you were wrong but you were right! Very symmetric set up:
(1**2)[8]+(2**2)[7]+(3**2)]6]+(4**2)[5]+(5**2)[4]+(6**2)[3]+(7**2)[2]+(8**2)[1] where () is the coefficient and [] square size
Also it can be figured out by just using the formula for the first n squares where n is 8.
Last edited by Graham Price; Wednesday, 24th September, 2014, 06:28 PM.
204 squares on a chessboard.
(8**2)+(7**2)+(6**2)+(5**2)+(4**2)+(3**2)+(2**2)+(1**2) -or- 64+49+36+25+16+9+4+1
This is the answer that would be rewarded in conventional classrooms with an A+. In other words, it's the stock, expected answer.
What if classrooms taught the art of thinking out of the box?
As the question was worded, the true answer is: there is an infinite number of squares on a chessboard.
Thinking out of the box:
The question wasn't worded: "How many squares are there on a chessboard which each contain an exact integer I = 1 to 64 of the existing drawn squares on the board?"
Therefore...
Does a square completely contained by the chessboard have to line up exactly with the borders of the existing dark and light squares on the chessboard?
Does a square completely contained by the chessboard have to be oriented at 0 degrees on the Cartesian plane? Isn't a square rotated N degrees still a square?
This may seem trivial... but people that naturally think like this without even having to be told to are in high demand and are the true creative geniuses, the inventors and problem solvers. As someone who has been through many technical interview processes, I can attest to how clever the questions can get to find the out-of-the-box thinkers.
This is a skill that some seem to be born with (not myself nor most people, unfortunately). But it is also a skill that can and should be taught and learned. It's like the picture of the vase... which if you look at it with an open mind, and are willing to see more than the vase, you find two profiles of human heads facing each other.
Some think that chess can and does teach these skills. I think to a certain extent it can and does, as do other games. I don't think chess is quite as special in this regard as some believe, and instead of a movement for teaching chess in schools, there should be a movement for teaching games of all kinds in schools, even -- gasp! -- poker (obviously with no money involved, just play chips).
And there are two major drawbacks to chess as a tool for teaching creativity:
(1) organized chess is too focused on winning and winners, and
(2) organized chess is too limited to 'just standard chess'. This actually stifles creativity. Not only should variants (the ones that offer decent game play) be encouraged in the entire world of organized chess, but young children should be taught to think of their own variants! Now THERE is some thinking out of the box!
Only the rushing is heard...
Onward flies the bird.
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