  The "pancake problem" asks how many prefix reversals are sufficient to sort
any permutation $\pi \in \mathcal{S}_k$ to the identity. We write $f(k)$ to
denote this quantity.
  The best known bounds are that $\frac{15}{14}k -O(1) \le f(k)\le
\frac{18}{11}k+O(1)$. The proof of the upper bound is computer-assisted, and
considers thousands of cases.
  We consider $h(k)$, how many prefix and suffix reversals are sufficient to
sort any $\pi \in \mathcal{S}_k$. We observe that $\frac{15}{14}k -O(1)\le
h(k)$ still holds, and give a human proof that $h(k) \le \frac{3}{2}k +O(1)$.
The constant "$\frac{3}{2}$" is a natural barrier for the pancake problem and
this variant, hence new techniques will be required to do better.
