Problem 329

We work from right to left as we would if doing this calculation by hand. In the units column, we have $L-4$ giving 1. Thus, $L=5$. (There is no borrowing required.) In the tens column, we have $0-N$ giving 1. Since 1 is larger than 0, we must borrow from the hundreds column. Thus, $10-N$ gives 1, which means $N=9$. In the hundreds column, we have $K-9$ but we have already borrowed 1 from $K$, so we have $(K-1)-9$ giving 0. Therefore, we must be subtracting 9 from 9, which means that $K$ should be 10, which is not possible. We can conclude, though, that $K=0$ and that we have borrowed from the 6. In the thousands column, we have $5-M=2$ or $M=3$. This gives $6005-3994=2011$, which is correct. Finally, $K+L+M+N=0+5+3+9=17$.