jmc

To divide 12 dimes into three piles with an odd number of dimes in each pile is to express 12 as a sum of three odd numbers. This is impossible to do, since $12=2\cdot 6$ is even and the sum of three odd integers is odd: $(2l+1)+(2m+1)+(2n+1)=2l+2m+2n+3=2(l+m+n+1)+1$. Therefore, there are $\boxed{0}$ ways to divide the dimes as described.