public class Q17587532
{
    static int[] GenerateDigitProducts( int max )
    {
        int sweep = 1;
        var results = new int[max+1];
        for( int i = 1; i <= 9; ++i ) results[i] = i;
        // loop invariant: all values up to sweep * 10 are filled in
        while (true) {
            int prior = results[sweep];
            if (prior > 0) {
                for( int j = 1; j <= 9; ++j ) {
                    int k = sweep * 10 + j; // <-- the key, generating number from digits is much faster than decomposing number into digits
                    if (k > max) return results;
                    results[k] = prior * j;
                    // loop invariant: all values up to k are filled in
                }
            }
            ++sweep;
        }
    }
    
    public static void Main()
    {
        int[] products = GenerateDigitProducts(99);
        
        for( int n = 21; n <= 99; ++n ) {
            System.Console.WriteLine(n.ToString("D2") + " => " + products[n].ToString("D3"));
        }
    }
}