R: Project Euler 1-9

problem1.R

f <- function(n) {
	x <- 999%/%n
	x * (x + 1) / 2 * n
}
f(3) + f(5) - f(15)

problem2.R

library(gmp)

answer <- 0
f <- fibnum(n <- 1)
while (f < 4000000) {
	if (f%%2 == 0) answer <- answer + f
	f <- fibnum(n <- n+1)
}
answer

problem3.R

library(gmp)
max(factorize(600851475143))

problem4.R

# code A

answer <- 0
for (a in 999:100) for (b in a:100) {
	x <- a*b
	if (x <= answer) break
	d <- x %/% (10^(floor(log10(x)):0)) %% 10
	if (all(d == rev(d))) answer <- x
}
answer

# code B

palindrome <- function(n) {
	x <- n %/% (10^(floor(log10(n)):0)) %% 10
	all(x == rev(x))
}

m <- matrix(c(999, 999, 999*999), 3)

repeat {
	max <- max(m[3,])
	top <- m[,which(m[3,] == max)]
	if (palindrome(top[3])) {print(top[3]); break}
	a <- top[1]-1
	b <- top[2]-1
	v <- append(m[,which(m[3,] != max)], c(top[1], b, top[1] * b))
	if (top[1] == top[2]) v <- append(v, c(a, a, a^2))
	m <- matrix(v, 3)
}

problem5.R

library(gmp)

Reduce(lcm.bigz, 1:20)

problem6.R

n <- 100
x <- n*(n+1)/2
y <- n*(n+1)*(2*n+1)/6
x*x-y

problem7.R

library(pracma)

n <- 10001
primes(n*log(n)+n*log(log(n)))[n]

problem8.R

s <- c(
	"73167176531330624919225119674426574742355349194934",
	"96983520312774506326239578318016984801869478851843",
	"85861560789112949495459501737958331952853208805511",
	"12540698747158523863050715693290963295227443043557",
	"66896648950445244523161731856403098711121722383113",
	"62229893423380308135336276614282806444486645238749",
	"30358907296290491560440772390713810515859307960866",
	"70172427121883998797908792274921901699720888093776",
	"65727333001053367881220235421809751254540594752243",
	"52584907711670556013604839586446706324415722155397",
	"53697817977846174064955149290862569321978468622482",
	"83972241375657056057490261407972968652414535100474",
	"82166370484403199890008895243450658541227588666881",
	"16427171479924442928230863465674813919123162824586",
	"17866458359124566529476545682848912883142607690042",
	"24219022671055626321111109370544217506941658960408",
	"07198403850962455444362981230987879927244284909188",
	"84580156166097919133875499200524063689912560717606",
	"05886116467109405077541002256983155200055935729725",
	"71636269561882670428252483600823257530420752963450"
)

xs <- as.numeric(unlist(strsplit(paste(s, collapse=""), "")))
prod5 <- function(n) prod(xs[n:(n+4)])
max(sapply(1:996, prod5))

problem9.R

a <- 1:331
b <- 2:499
 
f <- function(a, b) a < b & a^2 + b^2 == (1000-a-b)^2
g <- function(a, b) a*b*(1000-a-b)
 
outer(a, b, g)[outer(a, b, f)]