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Digit Deletion

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

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.

 

 

This problem is taken from the UKMT Mathematical Challenges.