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The cube, 41063625 (345

^{3}), can be permuted to produce two other cubes: 56623104 (384^{3}) and 66430125 (405^{3}). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.Find the smallest cube for which exactly five permutations of its digits are cube.—

I tried to generate all the cubic number with specific length, and iterate until exactly five numbers have the same digits.

^{?}View Code RSPLUS

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getCubicNumber <- function(ndigit) { lower <- floor(10^((ndigit-1)/3)) upper <- floor(10^(ndigit/3)) cube <- (lower:upper)^3 return(cube) } cubicPermutation <- function(nperm) { ndigit <- 1 flag <- TRUE while(flag) { ndigit <- ndigit+1 cubeNumber <- getCubicNumber(ndigit) cube <- sapply(as.character(cubeNumber), function(i) paste(sort(unlist(strsplit(i, split=""))), collapse="")) cnt <- table(cube) d <- names(cnt[cnt == nperm]) if (length(d)) { permDigits <- lapply(d, function(i) names(cube[cube==i])) res <- min(sapply(permDigits, min)) flag <- FALSE } } return(res) } cat("Answer of PE 62: ", cubicPermutation(5), "\n") |

This code runs in half a second.

> system.time(source("problem62.R")) Answer of PE 62: 127035954683 user system elapsed 0.414 0.001 0.416

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