Missing Digit

             A three digit number consists of 9, 5 and one more number. When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit?

Answer:  4. Let the digit unknown be n.

The given numbers is then 900+ 50 + n = 950 + n

When reversed the new number is 100n + 50 +9 =59 + 100n.

Subtracting these two numbers us get891 – 99n.

The digits can be arranged in 3 ways or 6 ways.

We have already investigated 2 of these ways.

We can now try one of the remaining 4 ways. One of these is n 95

100n + 90+ 5 =891 -99n

Or 199n = 796

 N=4

The unknown digit is 4.