The answer is 87912. There isn't much explanation to this...but I'll explain it anyways... NOMAD x 4 = DAMON 1. NOMAD < 25000 (anything above would return you a 6 digit number) 2. N cannot equal 1 (nothing multiplied by 4 equals 1) 3. N cannot equal 0 (if it did, D would have to be 5 since 5 is the only number that returns a 0 when multiplied by 4...but no 4 digit number multiplied by 4 equals a 5 digit number beginning with 5) 4. N must equal 2 5. D must equal 8 or 3 (they are the only numbers that return a 2 when multiplied by 4) 6. D cannot equal 3 (no 5 digit number multiplied by 4 equals a 5 digit number starting with 3) 7. D must equal 8 8. I gotta go for now...I'll finish explaining it later today...