Oddly Enough Puzzle

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How To Play Oddly Enough

Each square must contain an odd number (denoted by the letter O), an even number (denoted by the letter E), or no number (denoted by the letter X). If a square contains an odd number, then there must be an odd number of odd numbers in the squares immediately surrounding it (including itself). Likewise, if a square contains an even number, then there must be an even number of even numbers in the squares immediately surrounding it (including itself). Initially provided squares that contain odd (or even) numbers will also indicate how many numbers are in the squares immediately surrounding it (including itself) are odd (or even).

For example, consider a 3x3 puzzle:

The 5 tells us that there must be 4 odd numbers in the 8 squares surrounding the five (since 5 is itself an odd number). If one tries to place these 4 odd numbers, one finds that they must be in the spots indicated in the solution (since each odd number must itself be surrounding by an odd number of odd numbers). The bottom right corner must then be even (because of the 2 above it) and the left side square must be an X, since it can't be odd or even.