 Solution

Consider learning and memory of the maps. Repeating an identical map can improve later scores through recall rather than the assigned program, and a skill learned using one program can transfer to another. Provide comparable familiarization before recording responses and use new, difficulty-matched maps on later afternoons. If all volunteers face the same map on a given afternoon, common map difficulty is absorbed by the afternoon block.

The balanced transitions in the proposed row-column design help with first-order carryover effects, but general practice, higher-order memory and program-dependent learning may still require an explicit interaction term or carryover effect in the analysis. Merely applying randomization to treatment labels cannot make these effects disappear.