Output for other arguments for tricnt
tricnt&> 54+i.6
47.75 55.75 51.75 61 55.75 65
???
Here's an algebraic solution:
telz=: 3 :0
zx=. <.-:y
zm=. 1+<.y%3
+/>.-:(1&{-y-+/) (,:<:)zm+i.1+zx-zm
)
telz&> 54+i.7
61 56 65 61 70 65 75
or tacit (mind line wrapping)
+/@:([: >.@-: (({:@]-(-+/)) [:(,: <:) >:@<.@%&3
([+i.@>:@-~)<.@-:))&> 54+i.7
61 56 65 61 70 65 75
On 27-05-13 17:08, Olivier N. wrote:
My son said that one of the students arrived at the correct answer of 61
without a computer. I can't believe this given the time it would require to
go through the answer space via pencil and paper (28^3). Is there a closed
form solution, or algebraic solution?
Yes, there is. All in all, it was quite easy to find but the
corr-ection factor that depends on the parities of zmin and zmax.
Enjoy:
tricnt =: 3 : 0
zmin =. 1+>.y%3
zmax =. -<.1-y%2
sumz =. zmin+zmax
corr =. (_1)^(1-2|zmin)*(1-2|sumz)
(_1r4*corr) + (1+zmax-zmin) * (-(y+1)%2) + (3*sumz%4) - 1r4
)
Not being confident yet with J syntax,
the last line is overfull of parentheses.
Sorry about this.
Regards.
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Met vriendelijke groet,
@@i = Arie Groeneveld
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