[ Decimal numeral system ]

Given the number 123456789101112131415...99100. Erase 100 digits so that the remaining number is the largest possible.

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Answer: 9999978596061...99100. When erasing 100 digits from this number, we will always get numbers with the same number of digits, so the first digits should be the largest possible. First, we erase 84 digits (the last of which is the digit 4 in the number 49) to get the number 999995051...5758596061...99100. We can erase 16 more digits. To have the digit following 99999 be the digit 9, we need to erase 19 digits; we cannot do this. We also cannot leave the digit 8: for this, we need to erase 17 digits. But we can leave the digit 7 by erasing 15 digits 505152535455565. After this, we are allowed to erase only one more digit; it should be the digit 5 of the number 58.