Toasting four slices in a three-slice pan

A pan fits at most three slices of bread at a time and toasts only the side touching it. One side takes one minute, flipping or swapping is instant, and a slice is finished once both sides are toasted. What is the least number of minutes needed to finish four slices?

3 minutes. Four slices have $8$ sides and the pan handles $3$ per minute, so at least $\lceil 8/3\rceil=3$ minutes. That is achievable: toast $A_1,B_1,C_1$, then $A_2,B_2,D_1$, then $C_2,D_2$.