37383940...9394 is a concatenation of all integers from 37 to 94.
From this 116-digit number you are requested to erase 77 digits to leave the biggest number possible.
Please provide both the result and the reasoning to get it.

The largest number is:
Nine hundred ninety undecillion nine hundred seventy-seven decillion eight hundred seventy-nine nonillion eight hundred eight octillion one hundred eighty-two septillion eight hundred thirty-eight sextillion four hundred eighty-five quintillion eight hundred sixty-eight quadrillion seven hundred eighty-eight trillion eight hundred ninety-nine billion ninety-one million nine hundred twenty-nine thousand three hundred ninety-four.
(999,977,879,808,182,838,485,868,788,899,091,929,394.)

By erasing 77 digits from the 116-digit number, the number remaining will be 39 digits in length. The largest decimal number will begin with as many of the highest decimal digits (9) as possible. Thus, all digits but the digits 9 are erased from 37 to 69 leaving 54 remaining digits. Erasing all the non-9 digits to the next digit 9 in 79 would result in more than 77 digits erased. The next highest digit would be 8, but erasing the string of non-8
digits between 69 and the next digit 8 would also result in more than 77 digits erased, thus the next highest would be 7. Erasing the non-7, non-8 and non-9 digits between 69 and 80 will result in seven additional digits erased, leaving eight additional numbers to erase. As the goal is to form the largest possible 39-digit number, erasing any eight 7s of the string of 7s brings the 8 and following digits closer to the beginning.

Posted by Dej Mar on 2011-06-27 17:30:02