A connected envy-free cake-cutting might take infinitely many queries to find. An EF1 allocation can always be found in finite time by…

A connected envy-free cake-cutting might take infinitely many queries to find. An EF1 allocation can always be found in finite time by checking all possible allocations, but this algorithm requires exponential run-time.

Open the “Contiguous EF1 allocation” section on Wikipedia →

Source: List of unsolved problems in fair division (CC BY-SA 4.0)