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
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.
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