Digit Deletion
What is the largest number of digits that could be erased from this 1000-digit number, to get a surprising result?
Age
11 to 14
Challenge level
Problem
Dominique wrote down the $1000$-digit number $20082008\ldots 2008$.
She then erased some digits and was suprised to find that the remaining digits added up to $2008$. What is largest number of digits that she could have erased?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 746
To erase the most possible, keep only enough 8s to make 2008
2008$\div$8 = 251
There are 1000 digits so only 250 8s. Need 250 8s and 4 2s = 254 digits
Erase the other 746