[ Arithmetic. Mental calculation, etc.]

From the ten-digit number 2946835107, five digits were erased. What is the largest number that could result from this?

#
It is more advantageous for larger digits to remain at the beginning of the number.

## Solution

As a result of the deletion, some five-digit number remains. If in the number 2946835107, the first digit is not deleted, then the resulting five-digit number will start with a two and, consequently, will be less than 98517. Therefore, the first digit must be deleted. The digit 9 needs to be kept, otherwise, the first digit of the five-digit number will be less than 9. Similarly, we continue the analysis: to make the second digit of the five-digit number as large as possible, we need to delete the digits 4 and 6, and keep the digit 8. Next, we need to delete the digit 3 (if we keep it, the five-digit number will be in the form 983.., i.e., it will be less than 98517). One more digit needs to be deleted, and a simple check shows that it is most advantageous to delete the zero.

## Answer

98517.00