# project euler – Problem 32

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We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital. The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital. Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital. HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

Very similar to what I implemented in Problem 41.

^{?}View Code RSPLUS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | vec2num <- function(vec) { m <- length(vec) n <- sum(10^(m:1-1) * vec) return(n) } j <- 9 p <- allPerms(j, max=prod(1:j)*j) s <- 0 for (i in 1:nrow(p)) { product <- vec2num(p[i,6:9]) if (vec2num(p[i,1:2]) * vec2num(p[i,3:5]) == product) { s <- c(s,product) } if (vec2num(p[i,1]) * vec2num(p[i,2:5]) == product) { s <- c(s,product) } } print(sum(unique(s))) |

> system.time(source("Problem32.R")) [1] 45228 user system elapsed 35.32 0.04 35.45

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