  When numbers are added in base $b$ in the usual way, carries occur. If two
random, independent 1-digit numbers are added, then the probability of a carry
is $\frac{b-1}{2b}$. Other choices of digits lead to less carries. In
particular, if for odd $b$ we use the digits $\{-(b-1)/2,
-(b-3)/2,...,...(b-1)/2\}$ then the probability of carry is only
$\frac{b^2-1}{4b^2}$. Diaconis, Shao and Soundararajan conjectured that this is
the best choice of digits, and proved that this is asymptotically the case when
$b=p$ is a large prime. In this note we prove this conjecture for all odd
primes $p$.
