What is the largest five digit number without repetition?
To create this number we clearly must choose from the set {1,2,3,4,5,6,7,8,9}. Now we can only use each number once so we must be smart about where we put these numbers. First, notice that the digit that carries the most value is the first one. So this must be the largest. So, we have 9_ _ _ _. Now we have reduced the problem to making the largest 4 digit number from the set {1,2,3,4,5,6,7,8}. We can use the same argument here, leading to 98 _ _ _. Repeating this multiple times we can see that the answer is 98765.
