# Project Euler, problem 4, palindromes

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.

Firstly I decided to try and solve the problem using two 2-digit numbers so I can understand how the creator of this problem got to 9009.

In about 15 minutes I was able to come up with this brute force hack:

```
public class Problem4 {
public static void main(String[] args) {
solve();
}
private static void solve() {
int highestPalindrome = 0;
for (int left = 99; left > 2; left--) {
for (int right = 99; right > 2; right--) {
int candidate = left * right;
if (isPalindrome(candidate)) {
System.out.println(format("Palindrome found! Using %d * %d = %d ", left, right, candidate));
if (candidate > highestPalindrome) {
highestPalindrome = candidate;
}
}
}
}
System.out.println("Highest palindrome is " + highestPalindrome);
}
private static boolean isPalindrome(int palindrome) {
String palindromeString = "" + palindrome;
String reversed = new StringBuilder(palindromeString).reverse().toString();
return palindromeString.equals(reversed);
}
}
```

Which gives the output of

```
Highest palindrome is 9009
```

Excellent, so we’re on the right track. The next thing I did was alter the loop statements to start at 999, which then prints the following

```
Highest palindrome is 906609
```

Which is the correct answer!

Any suggestions on improvements? Please comment!