Thanks Jhe! That was fun solving this puzzle! I have a few alphametics puzzles in my own personal collection, and also "arithmetical restoration" puzzles, or as the famous English puzzliist H.E. Dudeney called them, "skeleton" puzzles. These are the ones where you start out with very few "given" digits, and the missing numbers are all replaced by question marks, X's, or asterisks. Happy Holidays!