The secret is in the common denominator of the summation of any two numbers whose digits are made from the same numbers.

Explanation: take 419. If you subtract something using the same numbers, you will always get something divisible by 9. Take these numbers:

419 - 491 = -72 / 9 = -8
419 - 194 = 225 / 9 = 25
419 - 941 = -522 / 9 = -58

Given this knowledge, we can take one of numbers away from the subtracted amount, add the remaining numbers, and subtract it from the next closes factor of 9.

Take the second one for instance.

419 - 194 = 225

If you exclude the "5", you solve by take the summation of the other two numbers, "2+2=4". Subtract 9 from 4 and you get "5", the missing number.

Same thing, exclude "2", you get "2+5=7". Subtract 9 from 7 and you get "2", the excluded number.

Here's something to remember though. If using larger numbers greater than 9, you need to subtract from the number divisible by 9 which is higher.

For instance, if you add the numbers and you get "21", you would need to subtract "27" (the next number higher than 21 divisible by 9) to get your answer of "6".

Thank you for taking me away from work for a few minutes. That was fun!