Q: Write down all the integers from 1 through 60 to form the number

123456789101112131415161718…495051525354555657585960.

Now delete 100 digits from this number.

Without rearranging the digits, what is the largest number possible?

A: Writing down all integers from 1 through 60 gives you a number 111 digits long:

9 numbers at 1 digit apiece: 9 digits

51 numbers at 2 digits apiece: 102 digits

Total: 111 digits.

If we’re not allowed to rearrange the digits, the largest number is:

99 999 785 960.