Here is what I think about this problem.
1) There are single digit numbers and two digit numbers . digits in all. We have to remove of these digits, leaving behind a digit number.
2) The largest digit must have as many s to begin with as possible. So, we drop the digits within the parenthesis – to begin with. So, the number begins with . And we have eliminated digits.
3) The number we end with at the end of this step is . We will have to eliminate more digits.
4) Typically, we jump to the conclusion here. We could remove and conclude that the answer should be . This is wrong.
5) We need to remove the s from instead. So, we eliminate the numbers within the parenthesis to create the number . This is the largest number possible.
5) Most of us get the general algorithm correct, but last minute twist makes it an absorbing exercise. Have fun !!!