I thought this was kinda cool! Here's my solution, its not robust or
probably efficient....
I'd to hear improvements or other solutions!
Justin
sq.test <- function(a, b) {
## test for number pairs that sum to squares.
sqrt(sum(a, b)) == floor(sqrt(sum(a, b)))
}
ok.pairs <- function(n, vec) {
## given n as a member of vec,
## which other members of vec satisfiy sq.test
vec <- vec[vec!=n]
vec[sapply(vec, sq.test, b=n)]
}
grow.seq <- function(y) {
## given a starting point (y) and a pairs list (pl)
## grow the squaring sequence.
ly <- length(y)
if(ly == y[1]) return(y)
## this line is the one that breaks down on other number sets...
y <- c(y, max(pl[[y[ly]]][!pl[[y[ly]]] %in% y]))
y <- grow.seq(y)
return(y)
}
## start vector
x <- 1:17
## get list of possible pairs
pl <- lapply(x, ok.pairs, vec=x)
## pick start at max since few combinations there.
y <- max(x)
grow.seq(y)
On Fri, Apr 13, 2012 at 2:34 PM, Ted Harding <ted.hard...@wlandres.net>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.
>
> NOTE: If there should happen to be some R package that can solve
> this kind of problem already, without you having to think much,
> then its use is illegitimate! (I.e. will be deemed "regurgitation").
>
> Over to you.
>
> With best wishes,
> Ted.
>
> -------------------------------------------------
> E-Mail: (Ted Harding) <ted.hard...@wlandres.net>
> Date: 13-Apr-2012 Time: 22:33:43
> This message was sent by XFMail
>
> ______________________________________________
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>
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