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The "pancake problem" asks how many prefix reversals are sufficient to sortany permutation $\pi \in \mathcal{S}_k$ to the identity. We write $f(k)$ todenote 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, andconsiders thousands of cases.  We consider $h(k)$, how many prefix and suffix reversals are sufficient tosort any $\pi \in \mathcal{S}_k$. We observe that $\frac{15}{14}k -O(1)\leh(k)$ 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 andthis variant, hence new techniques will be required to do better.

A new upper bound to (a variant of) the pancake problem