  We derive exactly the number of Hamiltonian paths H(n) on the two dimensional
Sierpinski gasket SG(n) at stage $n$, whose asymptotic behavior is given by
$\frac{\sqrt{3}(2\sqrt{3})^{3^{n-1}}}{3} \times (\frac{5^2 \times 7^2 \times
17^2}{2^{12} \times 3^5 \times 13})(16)^n$. We also obtain the number of
Hamiltonian paths with one end at a certain outmost vertex of SG(n), with
asymptotic behavior $\frac {\sqrt{3}(2\sqrt{3})^{3^{n-1}}}{3} \times (\frac {7
\times 17}{2^4 \times 3^3})4^n$. The distribution of Hamiltonian paths on SG(n)
with one end at a certain outmost vertex and the other end at an arbitrary
vertex of SG(n) is investigated. We rigorously prove that the exponent for the
mean $\ell$ displacement between the two end vertices of such Hamiltonian paths
on SG(n) is $\ell \log 2 / \log 3$ for $\ell>0$.
