Removing Digits
THE CHALLENGE
Which ten digits would you remove (they don’t need to be next to each other) from the number 1234512345123451234512345 to make the new number as large as possible? Which ten digits would you remove to make it as small as possible?
1234512345123451234512345
EXPLORATION
Can you think of other interesting problems similar to this one?
Notes
THE CHALLENGE
To make the number as large as possible, the highest priority has to be putting 5’s in the high order digits. So, start by removing 1 to 4 the first two times. Removing those 8 digits produces the number 55123451234512345. Removing the next 1 and 2 is the best you can do, and that produces the answer:
553451234512345
To make the smallest number, we want it to start with 1’s. Removing 8 digits by removing the first two groups of 2 to 5 produces the number 11123451234512345. The best we can do is remove the next 4 and 5, and that produces the answer
111231234512345
EXPLORATION
Similar puzzles can be made using different sequences of digits. The theme for all of them is that the highest order digits are the most important.