October 2017 Brain Puzzler Solution

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.

So deleting 100 digits leaves us with 11 digits.  It’s be best to have as many 9’s as we can as far to the left as we can. But there’s only 6 of those, and one of them is already in the hundreds place before we do any deleting.
If we’re not allowed to rearrange the digits, the largest number is:
99 999 785 960.

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