# Project Euler Q4 :: Largest palindrome product

Explanation. Standard caveat: don’t look here if you are trying to do these yourself.

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.

This seems like another brute-force question. There’s not that many numbers to test.

## check the worked solution
91*99 
## [1] 9009

I’m not aware of an is.palindrome function, but it’s easy enough to code.

is.palindrome <- function(x) {
## convert to character and explode
x <- unlist(strsplit(as.character(x), ""))
## check if the vector is palindromic
return(identical(x, rev(x)))
}
is.palindrome(9009)
## [1] TRUE
is.palindrome(9001)
## [1] FALSE

Let’s try it out for the two digit example and make sure we’re on the right track. Multiply all two digit numbers together and test them for palindrome-ness, then find the largest of those.

twodigits <- 10:99
prods <- expand.grid(twodigits, twodigits)
prods$prod <- prods[ ,1]*prods[ ,2] prods.palindromes <- prods$prod[sapply(prods$prod, is.palindrome)] max(prods.palindromes) ## [1] 9009 Great! What about three digits? threedigits <- 100:999 prods <- expand.grid(threedigits, threedigits) prods$prod <- prods[ ,1]*prods[ ,2]
prods.palindromes <- prods$prod[sapply(prods$prod, is.palindrome)]
largest <- max(prods.palindromes)
largest
## [1] 906609
### CORRECT

Takes a little longer, and generates a nice little 10MB, 810,000 element vector along the way.

format(object.size(prods), units="Mb")
## [1] "9.4 Mb"

The two three digit numbers?

prods[prods\$prod==largest, ]
##        Var1 Var2   prod
## 732594  993  913 906609
## 804514  913  993 906609

devtools::session_info()

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