23. Consider the 800 -digit integer
$$
234523452345 \cdots 2345 .
$$

The first $m$ digits and the last $n$ digits of the above integer are crossed out so that the sum of the remaining digits is 2345 . Find the value of $m+n$.
23. Ans: 130
Note that $2+3+4+5=14$. Thus the sum of the 800 digits is $200 \times 14=2800$. Thus we need to cross out digits with a sum equal to $2800-2345=455$.
Observe that $455=32 \times 14+7$. Thus we have to cross out 32 blocks of four digits ' 2345 ' either from the front or the back, a ' 2 ' from the front that remains and a ' 5 ' from the back that remains. Thus, $m+n=32 \times 4+2=130$.