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.

A:
983 + 86 + 8 = 1077
writing it vertically helps a lot
The B has to be a 1 as the total would be over 1000 and the M has to be a 9 as we are only adding a two digit and 1 digit number and getting over 1000

the last column must be adding up to 17 rather than 7 (otherwise S + A would be 4 and would be 1 and 3 but 3 is already used)
so S + A = 14 and since there will be a carry the next column over A + A + 1 will equal 17
so A = 8 and therefore A = 6