On Fri, Apr 13, 2012 at 10:34:49PM +0100, Ted Harding wrote:
> Greetings all!
> A recent news item got me thinking that a problem stated
> therein could provide a teasing little exercise in R
> programming.
>
> http://www.bbc.co.uk/news/uk-england-cambridgeshire-17680326
>
> Cambridge University hosts first European 'maths Olympiad'
> for girls
>
> The first European girls-only "mathematical Olympiad"
> competition is being hosted by Cambridge University.
> [...]
> Olympiad co-director, Dr Ceri Fiddes, said competition questions
> encouraged "clever thinking rather than regurgitating a taught
> syllabus".
> [...]
> "A lot of Olympiad questions in the competition are about
> proving things," Dr Fiddes said.
>
> "If you have a puzzle, it's not good enough to give one answer.
> You have to prove that it's the only possible answer."
> [...]
> "In the Olympiad it's about starting with a problem that anybody
> could understand, then coming up with that clever idea that
> enables you to solve it," she said.
>
> "For example, take the numbers one up to 17.
>
> "Can you write them out in a line so that every pair of numbers
> that are next to each other, adds up to give a square number?"
>
> Well, that's the challenge: Write (from scratch) an R program
> that solves this problem. And make it neat.
Hi.
Is recursion acceptable? Using recursion, i obtained
two solutions.
extend <- function(x)
{
y <- setdiff((1:17), x)
if (length(y) == 0) {
cat(x, "\n")
return
}
y <- y[(y + x[length(x)]) %in% (1:5)^2]
for (z in y) {
extend(c(x, z))
}
}
for (i in 1:17) extend(i)
16 9 7 2 14 11 5 4 12 13 3 6 10 15 1 8 17
17 8 1 15 10 6 3 13 12 4 5 11 14 2 7 9 16
Petr.
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