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] 9009I’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] TRUEis.palindrome(9001)## [1] FALSELet’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$prod, is.palindrome)]
max(prods.palindromes)## [1] 9009Great! What about three digits?
threedigits <- 100:999
prods <- expand.grid(threedigits, threedigits)
prods$prod <- prods[ ,1]*prods[ ,2]
prods.palindromes <- prods$prod[sapply(prods$prod, is.palindrome)]
largest <- max(prods.palindromes)
largest## [1] 906609### CORRECTTakes 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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