41 lines
844 B
Ruby
41 lines
844 B
Ruby
descr=%{
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Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
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21 22 23 24 25
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20 7 8 9 10
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19 6 1 2 11
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18 5 4 3 12
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17 16 15 14 13
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It can be verified that the sum of the numbers on the diagonals is 101.
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What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
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}
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reflexion=%{
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We can remark:
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1 +
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(1+2) + (1+2*2) + (1+3*2) + (1+4*2) +
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// let x be the last calulcated number (1+4*2)
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(x+4) + (x+2*4) + (x+3*4) + (x+4*4) +
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// let y be the last calulcated number (x+4*4)
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(y+6) + (y+2*6) + (y+3*6) + (y+4*6) +
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...
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}
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size=1001
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max=size**2
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n=1
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sum=0
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step=2
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while n<max
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(1..4).each do |s|
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n+=step
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# puts n
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sum+=n
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end
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step+=2
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end
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puts sum+1
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