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Discussion Starter #1
Consider a chess board...8 x8 squares. Disregard the fact of black or white, only 64 squares.

Take 8 chess or draught /checker men, place them on the board, one to each line so that no piece is in the same line horizontally, vertically or diagonally.

How many times can it be done ?

fred

" one potato, two potato, three potato, four "
 

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Fools rush in ....

Ooooohhhhh! My brain hurts!!!

Right now 44 members have viewed this (or the same member has viewed it 43 times - me making the 44th) but no-one has taken a shot at it. According to the old saying "fools rush in where wise men fear to tread" so "if the cap fits ......" so I will give it a go. (Jester)

I thought it was easy when I first read the question, but quickly realised it is fiendishly difficult (unless you know the answer!). I thought the answer would be based on a factorial number and played around with that idea before totally losing the plot. I also thought about prime numbers as they seem to be in all sorts of places where you don't expect them but got nowhere with that idea either.

Having given up on logic, my instinct tells me that the answer is 8. I can't justify this but that is my guess.

Brian
 

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Discussion Starter #4
It's amazing what happens when google can't help.

fred

" the square of the hypoteneuse ... has nothing to do with it "
 

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Sorry Mermaid but it can be done at least one time like this:

o represents empty space and X represents a draught:

ooooooxo
ooxooooo
oooooxoo
ooooooox
ooooxooo
oxoooooo
oooxoooo
xooooooo

But I have just had a clue how to work this out now (maybe!)

Brian
 

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The clue has slipped out of my grasp but there are definitely a lot of valid combinations. I think I was on the right line with factorials but I don't think it is factorial 8 as some combinations are not valid. I am too dim to work it out other than by sheer brute force checking all combinations but have something else to do over the next couple of days. It is probably factorial 8 minus something or other.

I only did maths to A level Fred, and spent most of my time in the sixth form bunking off and only just scraped through. I knew I would suffer as a result sooner or later! (LOL)

Come on there must be at least one mathematician out there somewhere. We can't let Fred beat us on this one!(Cloud)

Brian
 

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Thanks Sebe,

Having read that I can see why I got a headache trying to find the answer. Now I have read it I have an evan better headache!

Brian
 

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Discussion Starter #11
92 times? My goodness, even the Googlers are incorrect. Keep trying Benjidog,out of 100 plus viewers you managed to get one of the answers.
Come on folks, no cheating now, it certainly beats sudoku.

fred.

" is equal to the sum of the squares....."
 

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Once, after you've placed all eight you've no more pieces left. (K)
 

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Discussion Starter #15
Gdynia, you are getting closer, how about a demo as did Benjidog? It is easier if you just put in numbers. e.g.

73685241 this copies Benjidog's little diagram.

fred

" pieces of eight "
 

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From the Benjidog scheme, there are 6 positions of the "x" that satisfy the conditions in the first and the last lines (12 in total) and 4 for each one of the other 6 lines (24 in total).
So 12+24=36.
Piero
 

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Fred,

I had to give up as the dog ate two of the draughts.

They were both white ones so I am hopeful of some white dog poo shortly. (*))

Brian
 

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In the first line you have 8 options, the second 7, the third 6 etc. Therefore, 8! must be the key. 8x7x6x5x4x3x2 = 10080. Now my brain hurts. OK I give up.......
 
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