  In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten
years ago via certain strange hypergeometric identities. For example, for any
prime $p>3$, we show that
$$\sum_{k=0}^{p-1}\frac{\binom{4k}{2k+1}\binom{2k}k}{48^k}\equiv0\pmod{p^2},$$
and $$
\sum_{k=0}^{p-1}\frac{\binom{2k}{k}\binom{3k}{k}}{24^k}\equiv\begin{cases}\binom{(2p-2)/3}{(p-1)/3}\pmod{p^2}\
&\mbox{if}\ p\equiv1\pmod{3},\\ p/\binom{(2p+2)/3}{(p+1)/3}\pmod{p^2}\
&\mbox{if}\ p\equiv2\pmod{3}.\end{cases} $$ We also obtain some other results
of such types.
